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• W3049042986 abstract "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. Since each CΓ is a subsupercoalgebra of K[G], its dual $$ {C}_{Gamma}^{ast }={S}_{Gamma} $$ is a (pseudocompact) superalgebra called the generalized Schur superalgebra. There is a natural superalgebra morphism πΓ : Dist(G) → SΓ such that the image of the distribution algebra Dist(G) is dense in SΓ. For the ideal $$ X{(T)}_l^{+}, $$ of all weights of fixed length l, the generators of the kernel of $$ {uppi}_{X{(T)}_l^{+}} $$ are described." @default.
• W3049042986 created "2020-08-21" @default.
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• W3049042986 date "2022-03-31" @default.
• W3049042986 modified "2023-10-10" @default.
• W3049042986 title "DONKIN–KOPPINEN FILTRATION FOR GL(m|n) AND GENERALIZED SCHUR SUPERALGEBRAS" @default.
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• W3049042986 doi "https://doi.org/10.1007/s00031-022-09714-y" @default.
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