WHY SHOULD THE LITTLEWOOD-RICHARDSON RULE BE TRUE?

被引：17

作者：

Howe, Roger ^{[1
]}

Lee, Soo Teck ^{[2
]}

机构：

[1] Yale Univ, Dept Math, New Haven, CT 06520 USA

[2] Natl Univ Singapore, Dept Math, Singapore 119076, Singapore

来源：

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY | 2012年 / 49卷 / 02期

关键词：

Littlewood-Richardson Rule; Pieri Rule; GL(n) tensor product algebra; (GL(n); GL(m))-duality; STANDARD MONOMIAL THEORY; CLASSICAL LIE-GROUPS; TENSOR-PRODUCTS; CONVEXITY PROPERTIES; BRANCHING-RULES; HONEYCOMB MODEL; REPRESENTATIONS; EIGENVALUES; ALGEBRAS; PROOF;

D O I：

10.1090/S0273-0979-2011-01358-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：187 / 236

页数：50

共 43 条

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