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Classification of simple strong Harish-Chandra modules over the Lie superalgebra of vector fields on $\C^{m|n}$

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arxiv 2106.04801 v2 pith:MR3SP7A2 submitted 2021-06-09 math.RT

classification math.RT
keywords simplemodulesuperalgebrafieldsharish-chandramodulesstrongvector
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abstract

In this paper, we classify simple strong Harish-Chandra modules over the Lie superalgebra $W_{m,n}$ of vector fields on $\C^{m|n}$. Any such module is the unique simple submodule of some tensor module $F(P,V)$ for a simple weight module $P$ over the Weyl superalgebra $\mathcal K_{m,n}$ and a simple weight module $V$ over the general linear superalgebra $\gl_{m,n}$.

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Classification of simple quasifinite modules for contact superconformal algebras with $N\ne4$

    math.RT 2025-01 conditional novelty 7.0 of 10

    Every simple quasifinite module of the contact superconformal algebra with N≠4 odd variables is a highest or lowest weight module or a quotient of a tensor module built from a finite-dimensional so_N module.

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