Schur-Weyl duality for higher levels

Details Schur-Weyl duality for higher levels Schur-Weyl duality for higher levels

2006-05-09

arxiv.org/abs/math/0605217v3

Selecta Math. 14 (2008), 1-57

Mathematics

Representation Theory

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

Scientific paper

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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