Centers of degenerate cyclotomic Hecke algebras and parabolic category 𝒪

Brundan, Jonathan

doi:10.1090/S1088-4165-08-00333-6

Centers of degenerate cyclotomic Hecke algebras and parabolic category $\mathcal O$
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by Jonathan Brundan

Represent. Theory 12 (2008), 236-259

DOI: https://doi.org/10.1090/S1088-4165-08-00333-6

Published electronically: July 29, 2008

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Abstract:

We prove that the center of each degenerate cyclotomic Hecke algebra associated to the complex reflection group of type $B_d(l)$ consists of symmetric polynomials in its commuting generators. The classification of the blocks of the degenerate cyclotomic Hecke algebras is an easy consequence. We then apply Schur-Weyl duality for higher levels to deduce analogous results for parabolic category $\mathcal O$ for the Lie algebra $\mathfrak {gl}_n(\mathbb {C})$.

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