Irreducibility of induced supermodules for general linear supergroups

František Marko

doi:10.1016/j.jalgebra.2017.10.006

Irreducibility of induced supermodules for general linear supergroups

František Marko

Penn State Hazleton

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

In this note we determine when an induced supermodule H_G ⁰(λ), corresponding to a dominant integral highest weight λ of the general linear supergroup G=GL(m|n), is irreducible. Using the contravariant duality given by the supertrace we obtain a characterization of irreducibility of Weyl supermodules V(λ). This extends the result of Kac ([12], [13]) who proved that, for ground fields of characteristic zero, V(λ) is irreducible if and only if λ is typical.

Original language	English (US)
Pages (from-to)	92-110
Number of pages	19
Journal	Journal of Algebra
Volume	494
DOIs	https://doi.org/10.1016/j.jalgebra.2017.10.006
State	Published - Jan 15 2018

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/j.jalgebra.2017.10.006

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title = "Irreducibility of induced supermodules for general linear supergroups",

abstract = "In this note we determine when an induced supermodule HG 0(λ), corresponding to a dominant integral highest weight λ of the general linear supergroup G=GL(m|n), is irreducible. Using the contravariant duality given by the supertrace we obtain a characterization of irreducibility of Weyl supermodules V(λ). This extends the result of Kac ([12], [13]) who proved that, for ground fields of characteristic zero, V(λ) is irreducible if and only if λ is typical.",

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AB - In this note we determine when an induced supermodule HG 0(λ), corresponding to a dominant integral highest weight λ of the general linear supergroup G=GL(m|n), is irreducible. Using the contravariant duality given by the supertrace we obtain a characterization of irreducibility of Weyl supermodules V(λ). This extends the result of Kac ([12], [13]) who proved that, for ground fields of characteristic zero, V(λ) is irreducible if and only if λ is typical.

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UR - https://www.scopus.com/pages/publications/85033568840#tab=citedBy

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DO - 10.1016/j.jalgebra.2017.10.006

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VL - 494

SP - 92

EP - 110

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Irreducibility of induced supermodules for general linear supergroups

Abstract

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