TY - JOUR

T1 - A combinatorial approach to Donkin-Koppinen filtrations of general linear supergroups

AU - Marko, František

N1 - Publisher Copyright:
© 2021 Taylor & Francis Group, LLC.

PY - 2021

Y1 - 2021

N2 - 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].

AB - 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].

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U2 - 10.1080/00927872.2021.1886303

DO - 10.1080/00927872.2021.1886303

M3 - Article

AN - SCOPUS:85102191454

SN - 0092-7872

VL - 49

SP - 2961

EP - 2975

JO - Communications in Algebra

JF - Communications in Algebra

IS - 7

ER -