Regular strongly typical blocks of $\mathcal{O}^{\mathfrak{q}}$

TL;DR

This paper proves an equivalence between certain blocks of the category O for the queer Lie superalgebra and the general linear Lie algebra using Harish-Chandra bimodules, advancing understanding of their representation theory.

Contribution

It establishes a categorical equivalence for regular strongly typical blocks of the queer Lie superalgebra with those of the Lie algebra gl_n, using Harish-Chandra bimodule techniques.

Findings

Regular strongly typical blocks are equivalent to gl_n blocks.

Harish-Chandra bimodules are key to establishing the equivalence.

Advances understanding of queer Lie superalgebra representations.

Abstract

We use the technique of Harish-Chandra bimodules to prove that regular strongly typical blocks of the category $\mathcal{O}$ for the queer Lie superalgebra $\mathfrak{q}_n$ are equivalent to the corresponding blocks of the category $\mathcal{O}$ for the Lie algebra $\mathfrak{gl}_n$.