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 gl(m|n) and 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.2010 Mathematics Subject Classification. 17B35; 15A66.