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- Professor
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Howe, Roger Professor
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Overview
Publications
selected publications
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academic article
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Gurevich, S., & Howe, R.
(2021).
Ranks for representations of GLn over finite fields, their agreement, and positivity of Fourier transform. Indagationes Mathematicae.
32(6), 1332-1371.
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Gurevich, S., & Howe, R.
(2020).
Rank and duality in representation theory. Japanese Journal of Mathematics.
15(2), 223-309.
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(2017).
An analogue of Springer fibers in certain wonderful compactifications. Journal of Algebra and Its Applications.
16(09), 1750172-1750172.
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Howe, R., Lávička, R., Lee, S. T., & Souček, V.
(2017).
A reciprocity law and the skew Pieri rule for the symplectic group. Journal of Mathematical Physics.
58(3), 031702-031702.
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Howe, R., Kim, S., & Lee, S. T
(2017).
Double Pieri algebras and iterated Pieri algebras for the classical groups. American Journal of Mathematics.
139(2), 347-401.
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HOWE, R., & ZIEGLER, F.
(2015).
Bohr density of simple linear group orbits. ERGODIC THEORY AND DYNAMICAL SYSTEMS.
35(3), 910-914.
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(2015).
Response to the Elizabeth Green Article. Notices of the American Mathematical Society.
62(05), 508-514.
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(2014).
The teachers institute approach to professional development. Mathematics Enthusiast.
11(1), 41-48.
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(2013).
Unipotent invariant matrices. Linear Algebra and Its Applications.
439(1), 196-210.
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(2013).
The Cuoco Configuration. American Mathematical Monthly.
120(10), 916-916.
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(2012).
Why should the Littlewood–Richardson Rule be true?. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY.
49(2), 187-236.
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(2010).
Quadratic Reciprocity and the Sign of the Gauss Sum via the Finite Weil Representation. International Mathematics Research Notices.
2010(19), 3729-3745.
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(2009).
Toric degeneration of branching algebras. Advances in Mathematics.
220(6), 1809-1841.
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(2008).
The Stability of Graded Multiplicity in the Setting of the Kostant-Rallis Theorem. Transformation Groups.
13(3-4), 617-636.
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(2007).
Bases for some reciprocity algebras I. Transactions of the American Mathematical Society.
359(09), 4359-4388.
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(2006).
Bases for some reciprocity algebras III. COMPOSITIO MATHEMATICA.
142(06), 1594-1614.
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Howe, R., & Lee, S. T.
(2006).
Bases for some reciprocity algebras II. Advances in Mathematics.
206(1), 145-210.
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(2005).
Nice error bases, mutually unbiased bases, induced representations, the Heisenberg group and finite geometries. Indagationes Mathematicae.
16(3-4), 553-583.
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(2005).
A basis for the
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Howe, R., Tan, E., & Willenbring, J. F.
(2004).
Stable branching rules for classical symmetric pairs. Transactions of the American Mathematical Society.
357(4), 1601-1626.
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(2002).
Eigendistributions for orthogonal groups and representations of symplectic groups. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK.
545(545), 121-166.
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Howe, R.
(2002).
Hermione Granger's Solution. Mathematics Teacher.
95(2), 86-89.
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Horvath, J., & Howe, R.
(2000).
The natural representation of the stabilizer of four subspaces. Transactions of the American Mathematical Society.
352(12), 5795-5815.
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(1999).
Degenerate Principal Series Representations of GLn(C) and GLn(R). Journal of Functional Analysis.
166(2), 244-309.
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(1996).
Projective Invariants of Four Subspaces. Advances in Mathematics.
118(2), 295-336.
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(1994).
Complex of maximal lattice free simplices. Mathematical Programming.
66(3), 273-281.
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Bárány, I., Howe, R., & Scarf, H. E.
(1994).
The complex of maximal lattice free simplices. Mathematical Programming.
66(1-3), 273-281.
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(1993).
Homogeneous functions on light cones: the infinitesimal structure of some degenerate principal series representations. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY.
28(1), 1-74.
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(1992).
Estimating Hecke eigenvalues of Siegel modular forms. DUKE MATHEMATICAL JOURNAL.
67(1), 219-240.
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(1992).
Géométrie des cônes aigus et application à la projection euclidienne sur la chambre de Weyl positive. Journal of Algebra.
149(2), 472-493.
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Bárány, I., Howe, R., & Lovász, L.
(1992).
On integer points in polyhedra: A lower bound. Combinatorica.
12(2), 135-142.
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(1991).
The Capelli identity, the double commutant theorem, and multiplicity-free actions. Mathematische Annalen.
290(1), 565-619.
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Howe, R., & Moy, A.
(1990).
Hecke algebra isomorphisms for GL(n) over a p-adic field. Journal of Algebra.
131(2), 388-424.
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(1990).
Erratum to: “Remarks on classical invariant theory”. Transactions of the American Mathematical Society.
318(2), 823-823.
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Oates-Williams, S., Howe, R. E., & Zoll, P. F.
(1989).
Letters to the Editor. American Mathematical Monthly.
96(8), 708-710.
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Howe, R.
(1989).
Transcending classical invariant theory. Journal of the American Mathematical Society.
2(3), 535-552.
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Howe, R.
(1989).
Asymptotics of dimensions of invariants for finite groups. Journal of Algebra.
122(2), 374-379.
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(1989).
Remarks on classical invariant theory. Transactions of the American Mathematical Society.
313(2), 539-570.
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(1989).
The unitary representation theory of GL(n) of an infinite discrete field. Israel Journal of Mathematics.
67(1), 67-81.
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Howe, R.
(1988).
Automatic continuity of concave functions. Proceedings of the American Mathematical Society.
103(4), 1196-1200.
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Howe, R.
(1987).
(GLn, GLm)-duality and symmetric plethysm. Proceedings - Mathematical Sciences.
97(1-3), 85-109.
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(1987).
Sections and extensions of concave functions. Journal of Mathematical Economics.
16(1), 53-64.
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Benson, D., Feit, W., & Howe, R.
(1986).
Finite Linear Groups, the Commodore 64, Euler and Sylvester. American Mathematical Monthly.
93(9), 717-719.
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(1986).
A Bang-Bang theorem for optimization over spaces of analytic functions. Journal of Approximation Theory.
47(2), 101-121.
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Howe, R.
(1984).
Correction to “Very Basic Lie Theory”. American Mathematical Monthly.
91(4), 247-247.
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Howe, R.
(1983).
Very Basic Lie Theory. American Mathematical Monthly.
90(9), 600-623.
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(1983).
Some examples of automorphic forms on Sp4. DUKE MATHEMATICAL JOURNAL.
50(1), 55-106.
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(1982).
Most convex functions are smooth. Journal of Mathematical Economics.
9(1-2), 37-39.
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Howe, R.
(1980).
On the role of the Heisenberg group in harmonic analysis. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY.
3(2), 821-843.
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Howe, R.
(1980).
Quantum mechanics and partial differential equations. Journal of Functional Analysis.
38(2), 188-254.
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(1979).
On some results of Strichartz and of Rallis and Schiffman. Journal of Functional Analysis.
32(3), 297-303.
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Howe, R. E., & Moore, C. C.
(1979).
Asymptotic properties of unitary representations. Journal of Functional Analysis.
32(1), 72-96.
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(1979).
Uniqueness and existence of Whittaker models for the metaplictic group. Israel Journal of Mathematics.
34(1-2), 21-37.
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(1977).
Some qualitative results on the representation theory ofGlnover ap-adic field. PACIFIC JOURNAL OF MATHEMATICS.
73(2), 479-538.
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Howe, R.
(1977).
Tamely ramified supercuspidal representations ofGln. PACIFIC JOURNAL OF MATHEMATICS.
73(2), 437-460.
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(1977).
Computing characters of tamely ramified p-adic division algebras. PACIFIC JOURNAL OF MATHEMATICS.
73(2), 461-478.
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(1977).
Kirillov theory for compact p-adic groups. PACIFIC JOURNAL OF MATHEMATICS.
73(2), 365-382.
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(1977).
On a connection between nilpotent groups and oscillatory integrals associated to singularities. PACIFIC JOURNAL OF MATHEMATICS.
73(2), 329-364.
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(1977).
On representations of discrete, finitely generated, torsion-free, nilpotent groups. PACIFIC JOURNAL OF MATHEMATICS.
73(2), 281-306.
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(1977).
The fourier transform for nilpotent locally compact groups: I. PACIFIC JOURNAL OF MATHEMATICS.
73(2), 307-328.
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Howe, R. E.
(1977).
Topics in harmonic analysis on solvable algebraic groups. PACIFIC JOURNAL OF MATHEMATICS.
73(2), 383-436.
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Howe, R., & Silberger, A.
(1976).
Any unitary principal series representation of ( G L ) n (GL)_{n} over a p p -adic field is irreducible. Proceedings of the American Mathematical Society.
54(1), 376-378.
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(1975).
Traces of commutators of integral operators. Acta Mathematica.
135(0), 271-305.
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Howe, R., & Silberger, A.
(1975).
Why any unitary principal series representation of S L n SL_n over a p p -adic field decomposes simply. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY.
81(3), 599-601.
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Howe, R.
(1974).
The Fourier transform and germs of characters (case of Gl n over ap-adic field). Mathematische Annalen.
208(4), 305-322.
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Travis, C. C.
(1973).
Comparison of eigenvalues for linear differential equations of order 2 n 2n. Transactions of the American Mathematical Society.
177(0), 363-374.
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(1973).
On the character of Weil’s representation. Transactions of the American Mathematical Society.
177(0), 287-298.
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Howe, R. E.
(1973).
On the principal series of Gl n extrm {Gl}_{n} over p p -adic fields. Transactions of the American Mathematical Society.
177(0), 275-286.
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Howe, R.
(1972).
The Brauer group of a compact Hausdorff space and $n$-homogeneous $Csp{ast} $-algebras. Proceedings of the American Mathematical Society.
34(1), 209-209.
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(1971).
Representation theory for division algebras over local fields (tamely ramified case). BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY.
77(6), 1063-1067.
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Douglas, R. G., & Howe, R.
(1971).
On the C ∗ C^* -algebra of Toeplitz operators on the quarterplane. Transactions of the American Mathematical Society.
158(1), 203-217.
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Gurevich, S., & Howe, R.
(2021).
Ranks for representations of GLn over finite fields, their agreement, and positivity of Fourier transform. Indagationes Mathematicae.
32(6), 1332-1371.
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chapter
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Gurevich, S., & Howe, R.
(2020).
The Pieri Rule for GL n Over Finite Fields. MATHEMATICAL RESULTS IN QUANTUM MECHANICS.
Operator Theory, Operator Algebras and Their Interactions with Geometry and Topology.
(pp. 313-332).
Springer International Publishing.
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(2017).
Small Representations of Finite Classical Groups. GEOMETRY AND REPRESENTATION THEORY OF REAL AND P-ADIC GROUPS.
Representation Theory, Number Theory, and Invariant Theory.
(pp. 209-234).
Springer International Publishing.
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(2017).
Standard Monomial Theory for Harmonics in Classical Invariant Theory. GEOMETRY AND REPRESENTATION THEORY OF REAL AND P-ADIC GROUPS.
Representation Theory, Number Theory, and Invariant Theory.
(pp. 265-302).
Springer International Publishing.
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(2014).
Pieri algebras and Hibi algebras in representation theory. GEOMETRY AND REPRESENTATION THEORY OF REAL AND P-ADIC GROUPS.
Symmetry: Representation Theory and Its Applications.
(pp. 353-384).
Springer New York.
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(2014).
Three Pillars of First Grade Mathematics, and Beyond. Li, Y., & Lappan, G. (Eds.),
Mathematics Curriculum in School Education.
(pp. 183-207).
Springer Netherlands.
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Howe, R.
(2012).
Traces of Commutators of Integral Operators – the Aftermath. MATHEMATICAL RESULTS IN QUANTUM MECHANICS.
Mathematical Methods in Systems, Optimization, and Control.
(pp. 221-231).
Springer Basel.
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Howe, R.
(2010).
On A Notion of Rank for Unitary Representations of the Classical Groups. Harmonic Analysis and Group Representation.
(pp. 224-331).
Springer Berlin Heidelberg.
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Bárány, I., Howe, R., & Scarf, H. E.
(2008).
The complex of maximal lattice free simplices. Herbert Scarf’s Contributions to Economics, Game Theory and Operations Research.
(pp. 155-163).
Palgrave Macmillan UK.
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Howe, R.
(2002).
Affine-like Hecke algebras and p-adic representation theory. GEOMETRIC ASPECTS OF FUNCTIONAL ANALYSIS.
Iwahori-Hecke Algebras and their Representation Theory.
(pp. 27-69).
Springer Berlin Heidelberg.
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Howe, R.
(1994).
The Invariants of Degree up to 6 of all n-ary m-ics. GEOMETRY AND REPRESENTATION THEORY OF REAL AND P-ADIC GROUPS.
Lie Theory and Geometry.
(pp. 335-348).
Birkhäuser Boston.
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Howe, R., & Tan, E. C.
(1992).
Applications to Analysis. Non-Abelian Harmonic Analysis.
(pp. 121-202).
Springer New York.
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Howe, R., & Tan, E. C.
(1992).
Asymptotics of Matrix Coefficients. Non-Abelian Harmonic Analysis.
(pp. 203-242).
Springer New York.
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Howe, R., & Tan, E. C.
(1992).
Preliminaries. Non-Abelian Harmonic Analysis.
(pp. 1-50).
Springer New York.
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Howe, R., & Tan, E. C.
(1992).
Representations of the Lie Algebra of SL(2, ℝ). Non-Abelian Harmonic Analysis.
(pp. 51-92).
Springer New York.
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Howe, R., & Tan, E. C.
(1992).
Unitary Representations of the Universal Cover of SL(2, ℝ). Non-Abelian Harmonic Analysis.
(pp. 93-120).
Springer New York.
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Howe, R., & Stone, R.
(1983).
Linear Complementarity and the Degree of Mappings. Homotopy Methods and Global Convergence.
(pp. 179-223).
Springer US.
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Howe, R.
(1983).
On a Class of Linear Complementarity Problems of Variable Degree. Homotopy Methods and Global Convergence.
(pp. 155-177).
Springer US.
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Howe, R.
(1981).
Automorphic forms of low rank. GEOMETRIC ASPECTS OF FUNCTIONAL ANALYSIS.
Lecture Notes in Mathematics.
(pp. 211-248).
Springer Berlin Heidelberg.
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Gurevich, S., & Howe, R.
(2020).
The Pieri Rule for GL n Over Finite Fields. MATHEMATICAL RESULTS IN QUANTUM MECHANICS.
Operator Theory, Operator Algebras and Their Interactions with Geometry and Topology.
(pp. 313-332).
Springer International Publishing.
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conference paper
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Howe, R.
(2016).
A linear algebra description of K-C G(C)/B-C for classical groups. ADVANCES IN QUANTUM COMPUTATION.
149-172.
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Howe, R., & Lee, S. T.
(2014).
Structure of holomorphic unitary representations: the case of U-2,U-2. ADVANCES IN QUANTUM COMPUTATION.
139-170.
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(2012).
On the Tendency Toward Convexity of the Vector Sum of Sets. ADVANCES IN GLOBAL OPTIMIZATION.
67-76.
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(1998).
Principal Covariants, Multiplicity-Free Actions, and the K-types of Holomorphic Discrete Series. GEOMETRY AND REPRESENTATION THEORY OF REAL AND P-ADIC GROUPS.
147-161.
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Howe, R.
(2016).
A linear algebra description of K-C G(C)/B-C for classical groups. ADVANCES IN QUANTUM COMPUTATION.
149-172.
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institutional repository document
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Gurevich, S., Hadani, R., & Howe, R.
(2008).
Quadratic reciprocity and the sign of the Gauss sum via the finite Weil representation
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Gurevich, S., Hadani, R., & Howe, R.
(2008).
Quadratic reciprocity and the sign of the Gauss sum via the finite Weil representation
Research
principal investigator on
investigator on
Teaching
teaching activities
- EDCI691 Research Instructor
Works By Students
chaired theses and dissertations
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Foran, Alexandra Lair (2018-08). Problem Posing to Promote Cognitive Flexibility in Mathematics Teacher Preparation Programs.
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Foran, Alexandra Lair (2018-08). Problem Posing to Promote Cognitive Flexibility in Mathematics Teacher Preparation Programs.
Background
education and training
- Ph.D. in Mathematics, University of California, Berkeley - (Berkeley, California, United States) 1969
awards and honors
- Award for Distinguished Public Service, conferred by American Mathematical Society - (Providence, Rhode Island, United States), 2006
- Members/Foreign Associates, conferred by National Academy of Sciences - (Washington D.C., District of Columbia, United States), 1994
- Fellow, conferred by American Academy of Arts and Sciences - (Cambridge, Massachusetts, United States), 1993
- Lester R Ford Award, conferred by Mathematical Association of America - (Washington D.C., District of Columbia, United States), 1984
- Fellowship, conferred by John Simon Guggenheim Memorial Foundation - (New York, New York, United States), 1983
Contact
first name
- Roger
has last name
- Howe
mailing address
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Texas A&M University
Teaching, Learning And Culture (Tlac)
4232 TAMU
College Station, TX 77843-4232
USA
Other
In the News
- rogerhowe@tamu.edu