2020/08/27 by Frantisek Marko, Marko, Frantisek
Mathematics · #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.RA #math.RT
paper · pdf · doi:10.48550/arxiv.2008.12239
arxiv created 2020/08/27 · arxiv updated 2020/08/28
For a general linear supergroup G=GL(m|n), we consider a natural isomorphism ϕ: G → U-× Gev × U+, 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 ϕ^*(xij) of the generators of K[G]. We describe a specific ordering of the dominant weights X(T)+ of GL(m|n) for which there exists a Donkin-Koppinen filtration of the coordinate algebra K[G]. Let Γ be a finitely generated ideal Γ of X(T)+ and OΓ(K[G]) be the largest Γ-subsupermodule of K[G] having simple composition factors of highest weights λ∈ Γ. We apply combinatorial techniques, using generalized bideterminants, to determine a basis of G-superbimodules appearing in Donkin-Koppinen filtration of OΓ(K[G]).