A bijection between Littlewood-Richardson tableaux and rigged configurations

被引：64

作者：

Kirillov A.N. ^{[1
]}

Schilling A. ^{[3
,4
]}

Shimozono M. ^{[2
]}

机构：

[1] Division of Mathematics, Graduate School of Science, Hokkaido University, Sapporo

[2] Department of Mathematics, Virginia Tech., Blacksburg

[3] Instituut voor Theoretische Fysica, Universiteit van Amsterdam, 1018 XE Amsterdam

[4] Department of Mathematics, University of California, Davis, CA 95616-8633, One Shields Avenue

来源：

Selecta Mathematica | 2002年 / 8卷 / 1期

基金：

美国国家科学基金会;

关键词：

Generalized Kostka polynomials; Littlewood-Richardson tableaux; Rigged configurations;

D O I：

10.1007/s00029-002-8102-6

中图分类号：

学科分类号：

摘要：

We define a bijection from Littlewood-Richardson tableaux to rigged configurations and show that it preserves the appropriate statistics. This proves in particular a quasi-particle expression for the generalized Kostka polynomials KλR(q) labeled by a partition λ and a sequence of rectangles R. The generalized Kostka polynomials are q-analogues of multiplicities of the irreducible GL(n, ℂ)-module Vλ of highest weight λ in the tensor product VR1 ⊗ ... ⊗ VRL. © Birkhäuser Verlag, Basel, 2002.

引用

页码：67 / 135

页数：68

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