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Representations of Lie superalgebras with fusion flags. (English) Zbl 07013530
Summary: We study the category of finite-dimensional representations for a basic classical Lie superalgebra \(\mathfrak g=\mathfrak g_0\oplus \mathfrak g_1\). For the ortho-symplectic Lie superalgebra \(\mathfrak g=\mathfrak{osp}(1,2n),\) we show that various objects in that category admit a fusion flag, that is, a sequence of graded \(\mathfrak g_0[t]\)-modules such that the successive quotients are isomorphic to fusion products. Among these objects we find fusion products of finite-dimensional irreducible \(\mathfrak g\)-modules, truncated Weyl modules and Demazure type modules. This result shows that the character of these types of representations can be expressed in terms of characters of fusion products and we prove that the graded multiplicities are given by products of \(q\)-binomial coefficents. Moreover, we establish a presentation for these types of fusion products in terms of generators and relations of the enveloping algebra.

MSC:
17 Nonassociative rings and algebras
16 Associative rings and algebras
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