On the Hecke algebras and the colored HOMFLY polynomial
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arXiv
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| Format: | Preprint |
| Published: |
2006
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| _version_ | 1866909244622635008 |
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| author | Lin, Xiao-Song Zheng, Hao |
| author_facet | Lin, Xiao-Song Zheng, Hao |
| contents | The colored HOMFLY polynomial is the quantum invariant of oriented links in $S^3$ associated with irreducible representations of the quantum group $U_q(\mathrm{sl}_N)$. In this paper, using an approach to calculate quantum invariants of links via cabling-projection rule, we derive a formula for the colored HOMFLY polynomial in terms of the characters of the Hecke algebras and Schur polynomials. The technique leads to a fairly simple formula for the colored HOMFLY polynomial of torus links. This formula allows us to test the Labastida-Mariño-Vafa conjecture, which reveals a deep relationship between Chern-Simons gauge theory and string theory, on torus links. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0601267 |
| institution | arXiv |
| publishDate | 2006 |
| record_format | arxiv |
| spellingShingle | On the Hecke algebras and the colored HOMFLY polynomial Lin, Xiao-Song Zheng, Hao Quantum Algebra Geometric Topology The colored HOMFLY polynomial is the quantum invariant of oriented links in $S^3$ associated with irreducible representations of the quantum group $U_q(\mathrm{sl}_N)$. In this paper, using an approach to calculate quantum invariants of links via cabling-projection rule, we derive a formula for the colored HOMFLY polynomial in terms of the characters of the Hecke algebras and Schur polynomials. The technique leads to a fairly simple formula for the colored HOMFLY polynomial of torus links. This formula allows us to test the Labastida-Mariño-Vafa conjecture, which reveals a deep relationship between Chern-Simons gauge theory and string theory, on torus links. |
| title | On the Hecke algebras and the colored HOMFLY polynomial |
| topic | Quantum Algebra Geometric Topology |
| url | https://arxiv.org/abs/math/0601267 |