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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2301.03316 |
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| _version_ | 1866929299697696768 |
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| author | Hird, Niall |
| author_facet | Hird, Niall |
| contents | In this paper we give an explicit presentation of the centre of the restricted rational Cherednik algebra $\overline{H}_c(S_n\wr\mathbb{Z}/\ell\mathbb{Z})$ for a particular choice of parameter $c$. More precisely, we describe the centre of the indecomposable blocks of $\overline{H}_c(S_n\wr\mathbb{Z}/\ell\mathbb{Z})$ in terms of generators and relations. The parameters $c$ for which this presentation is valid are such that the Calogero-Moser space is smooth. Furthermore, we demonstrate how the explicit presentation of the centre of $\overline{H}_c(S_n\wr\mathbb{Z}/\ell\mathbb{Z})$ can be directly derived from the set of $\ell$-multipartitions of $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_03316 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An explicit presentation of the centre of the restricted rational Cherednik algebra Hird, Niall Representation Theory In this paper we give an explicit presentation of the centre of the restricted rational Cherednik algebra $\overline{H}_c(S_n\wr\mathbb{Z}/\ell\mathbb{Z})$ for a particular choice of parameter $c$. More precisely, we describe the centre of the indecomposable blocks of $\overline{H}_c(S_n\wr\mathbb{Z}/\ell\mathbb{Z})$ in terms of generators and relations. The parameters $c$ for which this presentation is valid are such that the Calogero-Moser space is smooth. Furthermore, we demonstrate how the explicit presentation of the centre of $\overline{H}_c(S_n\wr\mathbb{Z}/\ell\mathbb{Z})$ can be directly derived from the set of $\ell$-multipartitions of $n$. |
| title | An explicit presentation of the centre of the restricted rational Cherednik algebra |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2301.03316 |