A combinatorial approach to Donkin-Koppinen filtrations of general linear supergroups

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For a general linear supergroup (Formula presented.) we consider a natural isomorphism (Formula presented.) where Gev is the even subsupergroup of G, and U –, U + are appropriate odd unipotent subsupergroups of G. We compute the action of odd superderivations on the images (Formula presented.) of the generators of (Formula presented.) extending results established in [8] and [7]. We describe a specific ordering of the dominant weights (Formula presented.) of (Formula presented.) for which there exists a Donkin-Koppinen filtration of the coordinate algebra (Formula presented.) Let (Formula presented.) be a finitely generated ideal (Formula presented.) of (Formula presented.) and (Formula presented.) be the largest (Formula presented.) -subsupermodule of (Formula presented.) having simple composition factors of highest weights (Formula presented.) We apply combinatorial techniques, using generalized bideterminants, to determine a basis of G-superbimodules appearing in Donkin-Koppinen filtration of (Formula presented.) considered initially in [9].

Original languageEnglish (US)
Pages (from-to)2961-2975
Number of pages15
JournalCommunications in Algebra
Issue number7
StatePublished - 2021

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


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