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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 \(\mathfrak{gl}(\ell |n - \ell)\).{
©2016 American Institute of Physics}

MSC:
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
17B20 Simple, semisimple, reductive (super)algebras
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