On the cocenter of the cyclotomic Hecke algebra of type $G(r,1,n)$

Jun Hu; Lei Shi

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arXiv · 2211.07069

On the cocenter of the cyclotomic Hecke algebra of type $G(r,1,n)$

Jun Hu·Lei Shi

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Abstract

In this paper, we construct some integral bases for the cocenter of the cyclotomic Hecke algebra $\mathscr{H}_{n,K}$ 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 $\mathscr{H}_{n,K}$ 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 $g_{w,C}$ 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.

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BibTeX RIS

Jun Hu, Lei Shi. 2022-11-14. On the cocenter of the cyclotomic Hecke algebra of type $G(r,1,n)$. https://arxiv.org/abs/2211.07069

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