Extended T-systems

TL;DR

This paper leverages q-character theory to derive short exact sequences and recurrence relations in quantum affine group representations, generalizing the T-system for types A and B.

Contribution

It introduces a new set of 3-term recurrence relations that extend the classical T-system within the framework of quantum affine groups.

Findings

Derived short exact sequences in representation categories

Established generalized recurrence relations including T-system as a special case

Enhanced understanding of quantum affine group representations

Abstract

We use the theory of q-characters to establish a number of short exact sequences in the category of finite-dimensional representations of the quantum affine groups of types A and B. That allows us to introduce a set of 3-term recurrence relations which contains the celebrated T-system as a special case.