Irreducibility of induced supermodules for general linear supergroups
| Autor: | František Marko |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Weyl module 010102 general mathematics Zero (complex analysis) Duality (optimization) 010103 numerical & computational mathematics Characterization (mathematics) 01 natural sciences Covariance and contravariance of vectors Irreducibility 0101 mathematics Supermodule Mathematics::Representation Theory Supergroup Mathematics |
| Zdroj: | Journal of Algebra. 494:92-110 |
| ISSN: | 0021-8693 |
| Popis: | 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 = G L ( 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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