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Schur-Weyl duality for higher levels

Jonathan Brundan·Alexander Kleshchev
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Abstract

We extend Schur-Weyl duality to an arbitrary level $l \geq 1$, the case $l=1$ recovering the classical duality between the symmetric and general linear groups. In general, the symmetric group is replaced by the degenerate cyclotomic Hecke algebra over $\C$ parametrized by a dominant weight of level $l$ for the root system of type $A_\infty$. As an application, we prove that the degenerate analogue of the quasi-hereditary cover of the cyclotomic Hecke algebra constructed by Dipper, James and Mathas is Morita equivalent to certain blocks of parabolic category $\mathcal{O}$ for the general linear Lie algebra.

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Jonathan Brundan, Alexander Kleshchev. 2008-08-08. Schur-Weyl duality for higher levels. https://arxiv.org/abs/math/0605217

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