Clifford and Weyl superalgebras and spinor representations

TL;DR

This paper constructs a new class of twisted generalized Weyl algebras encompassing superalgebras and Lie superalgebra quotients, analyzing their representations and structural properties.

Contribution

It introduces a family of twisted generalized Weyl algebras including superalgebras and provides conditions for faithful differential operator representations.

Findings

Construction of twisted generalized Weyl algebras including superalgebras

Criteria for faithful differential operator representations

Description of graded support via pattern-avoiding vector compositions

Abstract

We construct a family of twisted generalized Weyl algebras which includes Weyl-Clifford superalgebras and quotients of the enveloping algebras of $\mathfrak{gl}(m|n)$ and $\mathfrak{osp}(m|2n)$. We give a condition for when a canonical representation by differential operators is faithful. Lastly, we give a description of the graded support of these algebras in terms of pattern-avoiding vector compositions.