Centers of degenerate cyclotomic Hecke algebras and parabolic category O
Abstract
Description
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.
26 pages; v3: theorem 2 strengthened slightly to compute dimensions block by block
26 pages; v3: theorem 2 strengthened slightly to compute dimensions block by block