Selecta Mathematica

, 8:67

A bijection between Littlewood-Richardson tableaux and rigged configurations

  • A. N. Kirillov
  • A. Schilling
  • M. Shimozono
Article

DOI: 10.1007/s00029-002-8102-6

Cite this article as:
Kirillov, A., Schilling, A. & Shimozono, M. Sel. math., New ser. (2002) 8: 67. doi:10.1007/s00029-002-8102-6

Abstract.

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 \( K_{\lambda R}(q) \) labeled by a partition \( \lambda \) and a sequence of rectangles R. The generalized Kostka polynomials are q-analogues of multiplicities of the irreducible \( GL(n, \mathbb{C}) \)-module \( V^\lambda \) of highest weight \( \lambda \) in the tensor product \( V^{R_1} \otimes \cdots \otimes V^{R_L} \).

Key words. Littlewood-Richardson tableaux, rigged configurations, generalized Kostka polynomials.

Copyright information

© Birkhäuser Verlag, Basel 2002

Authors and Affiliations

  • A. N. Kirillov
    • 1
  • A. Schilling
    • 2
  • M. Shimozono
    • 4
  1. 1.Division of Mathematics, Graduate School of Science, Hokkaido University, Sapporo, 060-0810, Japan, e-mail: kirillov@math.nagoya-u.ac.jpJP
  2. 2.Instituut voor Theoretische Fysica, Universiteit van Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, The NetherlandsNL
  3. 3.Department of Mathematics, University of California, One Shields Avenue, Davis, CA 95616-8633, USA, e-mail: anne@math.ucdavis.eduUS
  4. 4.Department of Mathematics, Virginia Tech, Blacksburg, VA 24061-0123, USA, e-mail: mshimo@math.vt.eduUS