On the Duflo-Serganova functor for the queer Lie superalgebra.(English)Zbl 1547.17017
The authors study the Duflo-Serganova functor \(\text{DS}_x:\mathrm{Rep}(\mathfrak{g})\rightarrow\mathrm{Rep}(\mathfrak{g}_x)\), where \(\mathfrak{g}_x:= \text{Ker }\text{ad}(x)/\text{Im } \text{ad}(x)\) for the queer Lie superalgebra \(\mathfrak{g} := \mathfrak{q}_n\) and for all odd \(x\) with \([x, x]\) semisimple. For the case when the rank of \(x\) is \(1\), the authors give a formula for multiplicities in terms of the arc diagram attached to a dominant weight \(\lambda\). They also prove that \(\text{DS}_x(L)\) is semisimple if \(L\) is a simple finite-dimensional module and \(x\) is of rank \(1\) satisfying \(x^2 = 0\).
Reviewer: Mee Seong Im (Baltimore)
MSC:
| 17B10 | Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) |
| 17B20 | Simple, semisimple, reductive (super)algebras |
| 17B55 | Homological methods in Lie (super)algebras |
Cite
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