Pieri algebras and Hibi algebras in representation theory Chapter

abstract

• Springer Science+Business Media New York 2014. A class of algebras that unify a variety of calculations in the representation theory of classical groups is discussed. Because of their relation to the classical Pieri Rule, these algebras are called double Pieri algebras. A generalization of the standard monomial theory of Hodge is developed for double Pieri algebras, that uses pairs of semistandard tableaux, rather than a single one. SAGBI theory and toric deformation are key tools. The deformed double Pieri algebras are described using a doubled version of GelfandTsetlin patterns. The approach allows the discussion to avoid dealing with relations between generators.

authors

• Howe, Roger

altmetric score

• 0.5

author list (cited authors)

• Howe, R.

citation count

• 3

complete list of authors

• Howe, Roger

Book Title

• Symmetry: Representation Theory and Its Applications

publication date

• January 2014

publisher

• Springer Nature  Publisher

published in

• Progress in Mathematics  Journal

keywords

• 49 Mathematical Sciences
• 4902 Mathematical Physics
• 4904 Pure Mathematics

Digital Object Identifier (DOI)

• 10.1007/978-1-4939-1590-3_13

International Standard Book Number (ISBN) 13

• 9781493915897

start page

• 353

end page

• 384

volume

• 257

URL

• http://dx.doi.org/10.1007/978-1-4939-1590-3_13