Harish-Chandra bimodules over rational Cherednik algebras
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arXiv
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| Format: | Preprint |
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2014
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| _version_ | 1866917710806384640 |
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| author | Simental, José |
| author_facet | Simental, José |
| contents | We study Harish-Chandra bimodules over the rational Cherednik algebra $H_{c}(W)$ associated to a complex reflection group $W$ with parameter $c$. Our results allow us to partially reduce the study of these bimodules to smaller algebras. We classify those pairs of parameters $(c,c')$ for which there exist fully supported Harish-Chandra bimodules, and give a description of the category of all Harish-Chandra bimodules modulo those without full support. When $W$ is a symmetric group we are able to classify all irreducible Harish-Chandra bimodules. Our proofs are based on localization techniques, the action of the Namikawa-Weyl group on the set of parameters, and the study of partial KZ functors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1409_5465 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | Harish-Chandra bimodules over rational Cherednik algebras Simental, José Representation Theory We study Harish-Chandra bimodules over the rational Cherednik algebra $H_{c}(W)$ associated to a complex reflection group $W$ with parameter $c$. Our results allow us to partially reduce the study of these bimodules to smaller algebras. We classify those pairs of parameters $(c,c')$ for which there exist fully supported Harish-Chandra bimodules, and give a description of the category of all Harish-Chandra bimodules modulo those without full support. When $W$ is a symmetric group we are able to classify all irreducible Harish-Chandra bimodules. Our proofs are based on localization techniques, the action of the Namikawa-Weyl group on the set of parameters, and the study of partial KZ functors. |
| title | Harish-Chandra bimodules over rational Cherednik algebras |
| topic | Representation Theory |
| url | https://arxiv.org/abs/1409.5465 |