## 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 C_{Γ} = O_{Γ}(K[G]). Here, the supermodule C_{Γ} 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^{–}×G_{ev}×U^{+} induces a superalgebra isomorphism ϕ^{*}K[U^{–}]⊗K[G_{ev}]⊗K[U^{+}]≃K[G]. We show that C_{Γ}=ϕ^{*}(K[U^{–}]⊗M_{Γ}K[U^{+}]), where M_{Γ}=O_{Γ}(K[G_{ev}]). Using the basis of the module M_{Γ}, given by generalized bideterminants, we describe a basis of C_{Γ}. Since each C_{Γ} 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 π_{Γ} : Dist(G) → S_{Γ} such that the image of the distribution algebra Dist(G) is dense in S_{Γ}. For the ideal X(T)l+, of all weights of fixed length l, the generators of the kernel of πX(T)l+ are described.

Original language | English (US) |
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Journal | Transformation Groups |

DOIs | |

State | Accepted/In press - 2022 |

## All Science Journal Classification (ASJC) codes

- Algebra and Number Theory
- Geometry and Topology