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HIGHEST WEIGHT HARISH-CHANDRA SUPERMODULES AND THEIR GEOMETRIC REALIZATIONS

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Abstract

In this paper we discuss the highest weight \( {\mathfrak{k}}_r \)-finite representations of the pair (𝔤r, \( {\mathfrak{k}}_r \)) consisting of 𝔤r, a real form of a complex basic Lie superalgebra of classical type 𝔤 (𝔤 ≠ A(n, n)), and the maximal compact subalgebra \( {\mathfrak{k}}_r \) of 𝔤r,0, together with their geometric global realizations. These representations occur, as in the ordinary setting, in the superspaces of sections of holomorphic super vector bundles on the associated Hermitian superspaces Gr/Kr.

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Authors and Affiliations

  1. DIME, Università di Genova, Via Armando Magliotto, 2, 17100, Savona, Italy

    C. CARMELI

  2. Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato, 5, 40126, Bologna, Italy

    R. FIORESI

  3. Department of Mathematics, University of California, Los Angeles, Los Angeles, CA, 90095-1555, USA

    V. S. VARADARAJAN

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  1. C. CARMELI
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  2. R. FIORESI
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CARMELI, C., FIORESI, R. & VARADARAJAN, V.S. HIGHEST WEIGHT HARISH-CHANDRA SUPERMODULES AND THEIR GEOMETRIC REALIZATIONS. Transformation Groups 25, 33–80 (2020). https://doi.org/10.1007/s00031-018-9499-0

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