Higher-dimensional Heegaard Floer homology and the polynomial representation of double affine Hecke algebras
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914144339361792 |
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| author | Gao, Yuan Reisin-Tzur, Eilon Tian, Yin Yuan, Tianyu |
| author_facet | Gao, Yuan Reisin-Tzur, Eilon Tian, Yin Yuan, Tianyu |
| contents | We show that the higher-dimensional Heegaard Floer homology between tuples of cotangent fibers and the conormal bundle of a homotopically nontrivial simple closed curve on $T^2$ recovers the polynomial representation of double affine Hecke algebra of type A. We also give a topological interpretation of Cherednik's inner product on the polynomial representation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06436 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher-dimensional Heegaard Floer homology and the polynomial representation of double affine Hecke algebras Gao, Yuan Reisin-Tzur, Eilon Tian, Yin Yuan, Tianyu Symplectic Geometry Geometric Topology Quantum Algebra Representation Theory We show that the higher-dimensional Heegaard Floer homology between tuples of cotangent fibers and the conormal bundle of a homotopically nontrivial simple closed curve on $T^2$ recovers the polynomial representation of double affine Hecke algebra of type A. We also give a topological interpretation of Cherednik's inner product on the polynomial representation. |
| title | Higher-dimensional Heegaard Floer homology and the polynomial representation of double affine Hecke algebras |
| topic | Symplectic Geometry Geometric Topology Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2511.06436 |