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Translated simple modules for Lie algebras and simple supermodules for Lie superalgebras

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 نشر من قبل Volodymyr Mazorchuk
 تاريخ النشر 2018
  مجال البحث
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We prove that the tensor product of a simple and a finite dimensional $mathfrak{sl}_n$-module has finite type socle. This is applied to reduce classification of simple $mathfrak{q}(n)$-supermodules to that of simple $mathfrak{sl}_n$-modules. Rough structure of simple $mathfrak{q}(n)$-supermodules, considered as $mathfrak{sl}_n$-modules, is described in terms of the combinatorics of category $mathcal{O}$.



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