On the cocenter of the cyclotomic Hecke algebra of type G(r,1,n) · arXivDesk
2211.07069Nov 14, 2022This paper is extracted from the previous preprint "Proof of the Center Conjectures for the cyclotomic Hecke and KLR algebras of type $A$", arXiv:2211.07069v6
On the cocenter of the cyclotomic Hecke algebra of type G(r,1,n)
In this paper, we construct some integral bases for the cocenter of the cyclotomic Hecke algebra Hn,K of type G(r,1,n) by generalizing Geck and Pfeiffer's work on the cocenters of the Iwahori-Hecke algebras associated to finite Weyl groups. We show that the dimensions of both the cocenter and the center of the cyclotomic Hecke algebra Hn,K
Nearby in the stack
are independent of the characteristic of the ground field, its Hecke parameter and cyclotomic parameters. As applications, we verify Chavli-Pfeiffer's conjecture on the polynomial coefficient
gw,C
for the complex reflection group of type
G(r,1,n)
and also show that both the cocenters and the centers of certain cyclotomic KLR algebras of affine type
A
are independent of the characteristic of the ground field.