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

The paper contains results that characterize the Donkin–Koppinen filtration of coordinate superalgebra K[G] general linear supergroup G = GL(m|n) by its subsupermodules CΓ OΓ(K[G]). Here, supermodule is largest subsupermodule whose composition factors are irreducible supermodules highest weight ⋋, where ⋋ belongs to a finitely-generated ideal Γ poset X(T)+ dominant weights G. A decomposition as product subsuperschemes U–×Gev×U+ induces isomorphism ϕ* K[U–]⊗K[Gev]⊗K[U+]≃K[G]. We show CΓ=ϕ*(K[U–]⊗MΓK[U+]), MΓ=OΓ(K[Gev]). Using basis module MΓ, given generalized bideterminants, we describe CΓ. Since each subsupercoalgebra K[G], dual $$ {C}_{\Gamma}^{\ast }={S}_{\Gamma} (pseudocompact) called Schur superalgebra. There natural morphism πΓ : Dist(G) → SΓ such image distribution algebra dense in SΓ. For X{(T)}_l^{+}, all fixed length l, generators kernel {\uppi}_{X{(T)}_l^{+}} described.