A bijection between Littlewood-Richardson tableaux and rigged configurations

TL;DR

This paper establishes a bijection between Littlewood-Richardson tableaux and rigged configurations, demonstrating the preservation of key statistics and providing a new combinatorial expression for generalized Kostka polynomials.

Contribution

It introduces a novel bijection that links two combinatorial models and proves their equivalence in representing generalized Kostka polynomials.

Findings

Bijection preserves relevant statistics

Provides a quasi-particle expression for Kostka polynomials

Connects tableaux and rigged configurations in representation theory

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.