DONKIN–KOPPINEN FILTRATION FOR GL(m|n) AND GENERALIZED SCHUR SUPERALGEBRAS

The paper contains results that characterize the Donkin–Koppinen filtration of the coordinate superalgebra K[G] of the general linear supergroup G = GL(m|n) by its subsupermodules CΓ = OΓ(K[G]). Here, the supermodule CΓ is the largest subsupermodule of K[G] whose composition factors are irreducible supermodules of highest weight ⋋, where ⋋ belongs to a finitely-generated ideal Γ of the poset X(T)+ of dominant weights of G. A decomposition of G as a product of subsuperschemes U–×Gev×U+ induces a superalgebra isomorphism ϕ*K[U–]⊗K[Gev]⊗K[U+]≃K[G]. We show that CΓ=ϕ*(K[U–]⊗MΓK[U+]), where MΓ=OΓ(K[Gev]). Using the basis of the module MΓ, given by generalized bideterminants, we describe a basis of CΓ.