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 ) 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 O \mathcal O for the Lie algebra g l n ( C ) \mathfrak {gl}_n(\mathbb {C}) .