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

Abstract

For a general linear supergroup we consider a natural isomorphism 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 of the generators of extending results established in [8] and [7]. We describe a specific ordering of the dominant weights of for which there exists a Donkin-Koppinen filtration of the coordinate algebra Let be a finitely generated ideal of and be the largest -subsupermodule of having simple composition factors of highest weights We apply combinatorial techniques, using generalized bideterminants, to determine a basis of G-superbimodules appearing in Donkin-Koppinen filtration of considered initially in [9].