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 $\mathfrak{q}(n)$ to a "$\mathbb{Z}\pm s$-weights" ($s\in \mathbb{C}$) 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 $\mathfrak{q}(n)$ and blocks of atypicality-one of the category of finite-dimensional modules for $\mathfrak{gl}(\ell|n-\ell)$.