Schur-Weyl duality for higher levels

Abstract

We extend Schur-Weyl duality to an arbitrary level $l\ge 1$, 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.

50 pages; v3: final version (no major changes)

References in corpus (1)

• Cyclotomic Nazarov-Wenzl algebras

Cited by in corpus (1)

• Highest weight theory for finite W-algebras