On the cocenter of the cyclotomic Hecke algebra of type $G(r,1,n)$
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866917416377778176 |
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| author | Hu, Jun Shi, Lei |
| author_facet | Hu, Jun Shi, Lei |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2211_07069 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the cocenter of the cyclotomic Hecke algebra of type $G(r,1,n)$ Hu, Jun Shi, Lei Representation Theory 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. |
| title | On the cocenter of the cyclotomic Hecke algebra of type $G(r,1,n)$ |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2211.07069 |