Donkin-Koppinen filtration for general linear supergroup

In this article we consider a generalization of Donkon-Koppinen filtrations for coordinate superalgebras of general linear supergroups. More precisely, if G = GL(m|n) is a general linear supergroup of (super)degree (m|n), then its coordinate superalgebra K[G] is a natural G × G-supermodule. For any finitely generated ideal Γ ⊆ Λ × Λ the largest supersubmodule OΓ(K[G]), whose all composition factors are L(λ)⊗L(μ) with (λ, μ) ∈ Γ, has a decreasing filtration OΓ(K[G]) = V0 ⊇ V1 ⊇ . . . , such that ⋂ t≥0 Vt = 0 and Vt/Vt+1 ≃ V−(λt) ⊗H −(λt). Here H 0 −(λ) and V−(λ) are couniversal and universal G-supermodules of highest weight λ ∈ Λ respectively (see [5]). We apply this result to describe adjoint action invariants of G.