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CLIFFORD AND WEYL SUPERALGEBRAS AND SPINOR REPRESENTATIONS

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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.

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Authors and Affiliations

  1. Department of Mathematics, Iowa State University, Ames, IA-50011, USA

    JONAS T. HARTWIG

  2. Department of Mathematics, University of California, Berkeley, CA-94720, USA

    VERA SERGANOVA

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  1. JONAS T. HARTWIG
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  2. VERA SERGANOVA
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Correspondence to JONAS T. HARTWIG.

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HARTWIG, J.T., SERGANOVA, V. CLIFFORD AND WEYL SUPERALGEBRAS AND SPINOR REPRESENTATIONS. Transformation Groups 25, 1185–1207 (2020). https://doi.org/10.1007/s00031-019-09542-7

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