Representations of quantum affine algebras of type $B_N$

TL;DR

This paper classifies finite-dimensional representations of quantum affine algebras of type B_N, showing that tame modules are exactly those with diagonalizable Cartan currents and describing their q-characters.

Contribution

It provides a complete classification of tame modules and their q-characters, linking them to super standard Young tableaux of type (2N|1).

Findings

Tame modules are exactly the thin modules with diagonalizable Cartan currents.

All such modules are classified explicitly.

q-characters are described using super standard Young tableaux.

Abstract

We study finite-dimensional representations of quantum affine algebras of type $B_N$. We show that a module is tame if and only if it is thin. In other words, the Cartan currents are diagonalizable if and only if all joint generalized eigenspaces have dimension one. We classify all such modules and describe their $q$-characters. In some cases, the $q$-characters are described by super standard Young tableaux of type $(2N|1)$.