Langlands branching rule for type B snake modules

TL;DR

This paper proves that snake modules for quantum Kac-Moody algebras of type B admit Langlands dual representations and provides an explicit formula for their character decompositions, confirming a conjecture by Frenkel and Hernandez.

Contribution

It establishes the Langlands duality for snake modules of type B and derives the explicit Langlands branching rule for their character decomposition.

Findings

Proved the existence of Langlands dual representations for snake modules.

Derived an explicit formula for character decomposition (Langlands branching rule).

Confirmed the conjecture by Frenkel and Hernandez.

Abstract

We prove that each snake module of the quantum Kac-Moody algebra of type $B_n^{(1)}$ admits a Langlands dual representation, as conjectured by Frenkel and Hernandez (Lett. Math. Phys. (2011) 96:217-261). Furthermore, we establish an explicit formula, called the Langlands branching rule, which gives the multiplicities in the decomposition of the character of a snake module of the quantum Kac-Moody algebra of type $B_n^{(1)}$ into a sum of characters of irreducible representations of its Langlands dual algebra.