### 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 | |

State | Published - Jan 15 2018 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Cite this

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**Irreducibility of induced supermodules for general linear supergroups.** / Marko, Frantisek.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Irreducibility of induced supermodules for general linear supergroups

AU - Marko, Frantisek

PY - 2018/1/15

Y1 - 2018/1/15

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85033568840&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85033568840&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2017.10.006

DO - 10.1016/j.jalgebra.2017.10.006

M3 - Article

AN - SCOPUS:85033568840

VL - 494

SP - 92

EP - 110

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -