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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.

17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
05E05 Symmetric functions and generalizations
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