KLR algebras and the branching rule II: the categorical Gelfand-Tsetlin basis for the classical Lie algebras

TL;DR

This paper develops a categorical framework for the branching rules of classical Lie algebras using KLR algebras, leading to a categorical Gelfand-Tsetlin basis for types B, C, and D.

Contribution

It constructs functors that categorify branching rules for classical Lie algebras and introduces a categorical Gelfand-Tsetlin basis for these types.

Findings

Categorical functors for branching rules are constructed.

A categorical Gelfand-Tsetlin basis is established.

Framework applies to types B, C, and D Lie algebras.

Abstract

We construct functors categorifying the branching rules for $U_q(\mathfrak{g})$ for $\mathfrak{g}$ of type $B_n$, $C_n$, and $D_n$ for the embeddings $so_{2n+1}\supset so_{2n-1}$, $sp_{2n}\supset sp_{2n-2}$, and $so_{2n}\supset so_{2n-2}$. We give the corresponding categorical Gelfand-Tsetlin basis.