Degenerate Affine Hecke-Clifford Algebras and Type $Q$ Lie Superalgebras

TL;DR

This paper classifies simple modules for degenerate affine Hecke-Clifford algebras and constructs an analogue of the Arakawa-Suzuki functor for type Q Lie superalgebras, advancing representation theory in superalgebra contexts.

Contribution

It provides a complete classification of simple integral modules and introduces new functorial constructions for type Q Lie superalgebras.

Findings

Complete classification of simple integral modules for AHCA.

Construction of an analogue of Zelevinsky's segment representations.

Development of an analogue of the Arakawa-Suzuki functor for type Q superalgebras.

Abstract

We construct the finite dimensional simple integral modules for the (degenerate) affine Hecke-Clifford algebra (AHCA). Our construction includes an analogue of Zelevinsky's segment representations, a complete combinatorial description of the simple calibrated modules, and a classification of the simple integral modules. Additionally, we construct an analogue of the Arakawa-Suzuki functor for the Lie superalgebra of type Q.