Supercharacters of queer Lie superalgebras.(English)Zbl 1417.17012
Summary: Let \(\mathfrak{g} = \mathfrak{g}_{\overline{0}} \oplus \mathfrak{g}_{\overline{1}}\) be the queer Lie superalgebra and let \(L\) be a finite-dimensional non-trivial irreducible \(\mathfrak{g}\)-module. Restricting the \(\mathfrak{g}\)-action on \(L\) to \(\mathfrak{g}_{\overline{0}}\), we show that the space of \(\mathfrak{g}_{\overline{0}}\)-invariants \(L^{\mathfrak{g}_{\overline{0}}}\) is trivial. As a consequence, we establish a conjecture first formulated by Gorelik, Grantcharov and Mazorchuk on the triviality of the supercharacter of irreducible \(\mathfrak{g}\)-modules in the case when the modules are finite dimensional.{
©American Institute of Physics}
©American Institute of Physics}
MSC:
| 17B20 | Simple, semisimple, reductive (super)algebras |
| 17B10 | Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) |
Cite
References:
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