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Classification of simple strong Harish-Chandra $W(m,n)$-modules

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arxiv 2006.05618 v2 pith:ISIXUJNH submitted 2020-06-10 math.RT

Yuly Billig , Vyacheslav Futorny , Kenji Iohara , Iryna Kashuba This is my paper · ORCID
classification math.RT
keywords modulessimplemoduletensorcuspidaleveryharish-chandrahighest
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abstract

We classify all simple strong Harish-Chandra modules for the Lie superalgebra $W(m,n)$. We show that every such module is either strongly cuspidal or a module of the highest weight type. We construct tensor modules for $W(m,n)$, which are parametrized by simple finite-dimensional $gl(m,n)$-modules and show that every simple strongly cuspidal $W(m,n)$-module is a quotient of a tensor module. Finally, we realize modules of the highest weight type as simple quotients of the generalized Verma modules induced from tensor modules for $W(m-1,n)$.

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Cited by 2 Pith papers

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

  1. Cuspidal modules over Superconformal algebras of rank \geq 1

    math.RT 2025-05 conditional novelty 7.0 of 10

    Cuspidal modules over all known superconformal algebras of rank at least one are classified, with the central charge vanishing except for one central extension of K(4).

  2. Whittaker Modules for W type Cartan Lie superalgebras

    math.RT 2025-11 conditional novelty 6.0 of 10

    Every simple non-singular Whittaker module of the Witt superalgebra W_{m,n} is a subquotient of a tensor module built from a finite-dimensional gl(m,n)-module.

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