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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.23456 |
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| _version_ | 1866909373213704192 |
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| author | Chalykh, Oleg Ryan, Bradley |
| author_facet | Chalykh, Oleg Ryan, Bradley |
| contents | This paper studies the spherical subalgebra of the double affine Hecke algebra of type $C^\vee C_n$ and relates it, at the classical level $q = 1$, to a certain character variety of the four-punctured Riemann sphere. This establishes a conjecture from math.QA/0504089. As a by-product, we find a completed phase space for the trigonometric van Diejen system, explicitly integrate its dynamics and explain how it can be obtained via Hamiltonian reduction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23456 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | DAHAs of Type $C^\vee C_n$ and Character Varieties Chalykh, Oleg Ryan, Bradley Representation Theory This paper studies the spherical subalgebra of the double affine Hecke algebra of type $C^\vee C_n$ and relates it, at the classical level $q = 1$, to a certain character variety of the four-punctured Riemann sphere. This establishes a conjecture from math.QA/0504089. As a by-product, we find a completed phase space for the trigonometric van Diejen system, explicitly integrate its dynamics and explain how it can be obtained via Hamiltonian reduction. |
| title | DAHAs of Type $C^\vee C_n$ and Character Varieties |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2410.23456 |