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.
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页码：187 / 236
页数：50
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