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Remarks on the Schur-Howe-Sergeev duality. (English) Zbl 0974.17031
The queer Lie superalgebra $$q(n)$$ is the direct sum of the general linear algebra $$\mathfrak{gl}(n)$$ and the adjoint module for $$\mathfrak{gl}(n)$$. Here the authors study a new Howe duality involving $$q(n)$$. They use Sergeev duality between $$q(n)$$ and a finite group which is a central extension of the hyperoctahedral group. They show how to use the Howe duality to re-derive Sergeev duality. Finally, they use this set up to give a representation theoretic realization of an identity involving Schur’s $$Q$$-functions.

##### MSC:
 17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras 05E05 Symmetric functions and generalizations
##### Keywords:
Lie superalgebra; Howe duality
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