A bijection between Littlewood-Richardson tableaux and rigged configurations

Abstract

A bijection is defined from Littlewood-Richardson tableaux to rigged configurations. It is shown that this map preserves the appropriate statistics, thereby proving a quasi-particle expression for the generalized Kostka polynomials, which are q-analogues of multiplicities in tensor products of irreducible general linear group modules indexed by rectangular partitions.

66 pages, AMS-LaTeX, requires xy.sty and related files

References in corpus (4)

• Fermionic Quasi-Particle Representations for Characters of $(G^{(1)}{)}_1\times (G^{(1)}{)}_1ø(G^{(1)}{)}_2$
• Inhomogeneous lattice paths, generalized Kostka polynomials and A${}_{n-1}$ supernomials
• Fermionic counting of RSOS-states and Virasoro character formulas for the unitary minimal series M(ν,ν+1). Exact results
• Spinon Bases, Yangian Symmetry and Fermionic Representations of Virasoro Characters in Conformal Field Theory

Cited by in corpus (2)

• Fermionic form and Betti numbers
• Paths and Kostka--Macdonald Polynomials