2020/08/14 by František Marko, Frantisek Marko, Marko, Frantisek +2
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.RA #math.RT
paper · pdf · doi:10.48550/arxiv.2008.06558
arxiv created 2020/08/14 · openalex publication_date 2020/08/14 · arxiv updated 2020/08/18 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
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 λ, where λ 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-]⊗ MΓ⊗ K[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 CΓ^*=SΓ 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 π_X(T)+l are described.