On the center of the generic affine Hecke algebra
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909554442240000 |
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| author | Cautis, Sabin Ollivier, Rachel |
| author_facet | Cautis, Sabin Ollivier, Rachel |
| contents | We identify the center of the generic affine Hecke algebra $H_q$ corresponding to some root datum with the semigroup algebra $\mathbb C[q][\check X^+]$ of the dominant chamber of its coweight lattice. This is done by first identifying a maximal commutative subalgebra $A_q \subset H_q$ with the Rees algebra associated to the semigroup algebra of the coweight lattice for the filtration induced by the length function. We explain how this subalgebra $A_q$ can also be identified with (quantum) cohomology of the toric variety given by the fan corresponding to the coroot lattice (a Hessenberg variety). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21097 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the center of the generic affine Hecke algebra Cautis, Sabin Ollivier, Rachel Representation Theory Rings and Algebras We identify the center of the generic affine Hecke algebra $H_q$ corresponding to some root datum with the semigroup algebra $\mathbb C[q][\check X^+]$ of the dominant chamber of its coweight lattice. This is done by first identifying a maximal commutative subalgebra $A_q \subset H_q$ with the Rees algebra associated to the semigroup algebra of the coweight lattice for the filtration induced by the length function. We explain how this subalgebra $A_q$ can also be identified with (quantum) cohomology of the toric variety given by the fan corresponding to the coroot lattice (a Hessenberg variety). |
| title | On the center of the generic affine Hecke algebra |
| topic | Representation Theory Rings and Algebras |
| url | https://arxiv.org/abs/2503.21097 |