Centers of degenerate cyclotomic Hecke algebras and parabolic category O

Details Centers of degenerate cyclotomic Hecke algebras and parabolic category O Centers of degenerate cyclotomic Hecke algebras and parabolic category O

2006-07-27

arxiv.org/abs/math/0607717v3

Represent. Theory 12 (2008), 236-259.

Mathematics

Representation Theory

26 pages; v3: theorem 2 strengthened slightly to compute dimensions block by block

Scientific paper

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 deduce that the center of an integral block of parabolic category O for the Lie algebra gl_n(C) is generated by the center of its universal enveloping algebra.

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