Proof of the combinatorial Kirillov-Reshetikhin conjecture

TL;DR

This paper provides a direct proof of the combinatorial Kirillov-Reshetikhin conjecture, establishing a key link between tensor product multiplicities of modules and restricted fermionic sums for simple Lie algebras.

Contribution

It offers the first direct proof of the combinatorial version of the Kirillov-Reshetikhin conjecture, confirming the relationship between generating functions and tensor product multiplicities.

Findings

Proves the equality of generating functions for tensor product multiplicities.

Confirms the combinatorial Kirillov-Reshetikhin conjecture for all simple Lie algebras.

Links tensor product multiplicities to restricted fermionic summations.

Abstract

In this paper we give a direct proof of the equality of certain generating function associated with tensor product multiplicities of Kirillov-Reshetikhin modules for each simple Lie algebra g. Together with the theorems of Nakajima and Hernandez, this gives the proof of the combinatorial version of the Kirillov-Reshetikhin conjecture, which gives tensor product multiplicities in terms of restricted fermionic summations.