Centers of degenerate cyclotomic Hecke algebras and parabolic category O

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 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.

arXiv comment26 pages; v3: theorem 2 strengthened slightly to compute dimensions block by block

References in corpus (1)

• Blocks of cyclotomic Hecke algebras

Cited by in corpus (7)

• Blocks of cyclotomic Hecke algebras
• Degenerate cyclotomic Hecke algebras and higher level Heisenberg categorification
• Affine wreath product algebras
• Singular blocks of parabolic category O and finite W-algebras
• Highest weight theory for finite W-algebras
• Modular representations and branching rules for wreath Hecke algebras
• Symmetric functions, parabolic category O and the Springer fiber