On the structure of tensor products of the finite-dimensional representations of quantum affine $\mathfrak{sl}_n$

TL;DR

This paper reviews the structure of tensor products of finite-dimensional representations of quantum affine rak{sl}_n, focusing on q-characters and introducing snake modules with their character formulas.

Contribution

It provides an elementary perspective on the tensor product structure, introduces snake modules, and connects classical Lie algebra representation theory to quantum affine algebra representations.

Findings

Analysis of tensor product structures in quantum affine rak{sl}_n

Introduction of snake modules and their character formulas

Clarification of the relationship between classical and quantum representation theories

Abstract

We review some important facts about the structure of tensor products of finite dimensional representations of quantum affine algebras. This is done from the elementary standpoint of the representation theory of semisimple Lie algebras in the scope of a masters thesis. We set the focus on drawing the line to the finite dimensional representation theory of quantum affine $\mathfrak{sl}_n$, the theory of q-characters, and introduce the so called snake modules together with their character formula.