CLIFFORD AND WEYL SUPERALGEBRAS AND SPINOR REPRESENTATIONS

Abstract

We construct a family of twisted generalized Weyl algebras which includes Weyl–Clifford superalgebras and quotients of the enveloping algebras of \( \mathfrak{gl}\left(m|n\right) \) and \( \mathfrak{osp}\left(m|2n\right) \). 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.