A note on double affine Hecke algebra for skein algebra on twice-punctured torus
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912008611299328 |
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| author | Hikami, Kazuhiro |
| author_facet | Hikami, Kazuhiro |
| contents | We construct a generalization of the $C^\vee C_1$-type double affine Hecke algebra for the skein algebra on the twice-punctured torus $Σ_{1,2}$ using the Heegaard dual of the Iwahori--Hecke operator recently introduced in our previous article. We show that the automorphisms of our algebra correspond to the Dehn twists about the curves on $Σ_{1,2}$. We also give the cluster algebraic construction of the the classical limit of the skein algebra, where the Dehn twists are given in terms of the cluster mutations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_17021 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on double affine Hecke algebra for skein algebra on twice-punctured torus Hikami, Kazuhiro Quantum Algebra Mathematical Physics Geometric Topology Representation Theory We construct a generalization of the $C^\vee C_1$-type double affine Hecke algebra for the skein algebra on the twice-punctured torus $Σ_{1,2}$ using the Heegaard dual of the Iwahori--Hecke operator recently introduced in our previous article. We show that the automorphisms of our algebra correspond to the Dehn twists about the curves on $Σ_{1,2}$. We also give the cluster algebraic construction of the the classical limit of the skein algebra, where the Dehn twists are given in terms of the cluster mutations. |
| title | A note on double affine Hecke algebra for skein algebra on twice-punctured torus |
| topic | Quantum Algebra Mathematical Physics Geometric Topology Representation Theory |
| url | https://arxiv.org/abs/2408.17021 |