# zbMATH — the first resource for mathematics

Reduction method for representations of queer Lie superalgebras. (English) Zbl 1386.17011
Summary: 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 $$\mathfrak{gl}(\ell |n - \ell)$$.{