WHY SHOULD THE LITTLEWOOD-RICHARDSON RULE BE TRUE? Academic Article

abstract

• We give a proof of the Littlewood-Richardson Rule for describing tensor products of irreducible finite-dimensional representations of GL n. The core of the argument uses classical invariant theory, especially (GL n, GL m)-duality. Both of the main conditions (semistandard condition, lattice permutation/ Yamanouchi word condition) placed on the tableaux used to define Littlewood-Richardson coefficients have natural interpretations in the argument. 2011 American Mathematical Society.

authors

• Howe, Roger

published proceedings

• BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY

altmetric score

• 0.5

author list (cited authors)

• Howe, R., & Lee, S. T.

citation count

• 16

complete list of authors

• Howe, Roger||Lee, Soo Teck

publication date

• May 2012

publisher

• American Mathematical Society (AMS)  Publisher

published in

• BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY  Journal

keywords

• (gl(n), Gl(m))-duality
• Gl(n) Tensor Product Algebra
• Littlewood-richardson Rule
• Pieri Rule

Digital Object Identifier (DOI)

• 10.1090/S0273-0979-2011-01358-1

start page

• 187

end page

• 236

volume

• 49

issue

• 2

URL

• http://dx.doi.org/10.1090/s0273-0979-2011-01358-1