Clifford and Weyl superalgebras and spinor representations

We construct a family of twisted generalized Weyl algebras which includes Weyl-Clifford superalgebras and quotients of the enveloping algebras of $\mathfrak{g}\mathfrak{l}(m\mathrm{\mid }n)$ and $\mathfrak{o}\mathfrak{s}\mathfrak{p}(m\mathrm{\mid }2n)$. 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.