Reduction method for representations of queer Lie superalgebras

Abstract

We develop a reduction procedure which provides an equivalence from an arbitrary block of the BGG category for the queer Lie superalgebra 𝔮(n) to a “ℤ ± s-weights” (s ∈ ℂ) block of a BGG category for finite direct sum of queer Lie superalgebras. We give descriptions of blocks. We also establish equivalences between certain maximal parabolic subcategories for 𝔮(n) and blocks of atypicality-one of the category of finite-dimensional modules for 𝔤𝔩(ℓ|n − ℓ).