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CHARACTER FORMULAE IN CATEGORY \( \mathcal{O} \) FOR EXCEPTIONAL LIE SUPERALGEBRAS D(2|1; ζ)

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Abstract

We establish character formulae for representations of the one-parameter family of simple Lie superalgebras D(2|1; ζ). We provide a complete description of the Verma flag multiplicities of the tilting modules and the projective modules in the BGG category \( \mathcal{O} \) of D(2|1; ζ)-modules of integral weights, for any complex parameter ζ. The composition factors of all Verma modules in \( \mathcal{O} \) are then obtained.

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Authors and Affiliations

  1. Institute of Mathematics, Academia Sinica, Taipei, Taiwan, 10617

    SHUN-JEN CHENG

  2. Department of Mathematics, University of Virginia, Charlottesville, VA, 22904, USA

    WEIQIANG WANG

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  1. SHUN-JEN CHENG
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  2. WEIQIANG WANG
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Correspondence to WEIQIANG WANG.

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CHENG, SJ., WANG, W. CHARACTER FORMULAE IN CATEGORY \( \mathcal{O} \) FOR EXCEPTIONAL LIE SUPERALGEBRAS D(2|1; ζ). Transformation Groups 24, 781–821 (2019). https://doi.org/10.1007/s00031-018-9506-5

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  • DOI: https://doi.org/10.1007/s00031-018-9506-5

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