Rigged Configurations and Kashiwara Operators

TL;DR

This paper proves that for types A^{(1)}_n and D^{(1)}_n, the rigged configuration bijection preserves the action of Kashiwara operators on tensor products of Kirillov-Reshetikhin crystals, establishing a key structural correspondence.

Contribution

It demonstrates that the rigged configuration bijection intertwines Kashiwara operators for specific types, advancing understanding of crystal bases and combinatorial models.

Findings

Rigged configuration bijection preserves Kashiwara operators.

Established correspondence for types A^{(1)}_n and D^{(1)}_n.

Clarifies structure of tensor products in crystal theory.

Abstract

For types $A^{(1)}_n$ and $D^{(1)}_n$ we prove that the rigged configuration bijection intertwines the classical Kashiwara operators on tensor products of the arbitrary Kirillov-Reshetikhin crystals and the set of the rigged configurations.