The q-characters of representations of quantum affine algebras and deformations of W-algebras

TL;DR

This paper introduces q-characters for finite-dimensional quantum affine algebra representations, linking them to deformed W-algebras, and explores their algebraic properties and connections to Bethe Ansatz.

Contribution

It defines q-characters for quantum affine algebras and establishes their algebraic structure and relation to deformed W-algebras, Bethe Ansatz, and screening operators.

Findings

q-characters form a homomorphism to a polynomial ring

Conjecture: the image equals the intersection of screening operators

Connection established between q-characters and Bethe Ansatz

Abstract

We propose the notion of q-characters for finite-dimensional representations of quantum affine algebras. It is motivated by our theory of deformed W-algebras. We show that the q-characters give rise to a homomorphism from the Grothendieck ring of representations of a quantum affine algebra to a polynomial ring. We conjecture that the image of this homomorphism is equal to the intersection of certain "screening operators". We also discuss the connection between q-characters and Bethe Ansatz.