On the Hecke algebras and the colored HOMFLY polynomial
| Autor: | Xiao-Song Lin, Hao Zheng |
|---|---|
| Rok vydání: | 2009 |
| Předmět: |
Pure mathematics
General Mathematics Quantum invariant Bracket polynomial String theory 01 natural sciences Mathematics - Geometric Topology High Energy Physics::Theory Mathematics::Quantum Algebra Mathematics - Quantum Algebra 0103 physical sciences FOS: Mathematics Quantum Algebra (math.QA) Gauge theory 0101 mathematics Mathematics::Symplectic Geometry Mathematics HOMFLY polynomial 010308 nuclear & particles physics Quantum group Applied Mathematics 010102 general mathematics Geometric Topology (math.GT) Mathematics::Geometric Topology Schur polynomial Irreducible representation |
| Zdroj: | Transactions of the American Mathematical Society. 362:1-18 |
| ISSN: | 0002-9947 |
| DOI: | 10.1090/s0002-9947-09-04691-1 |
| Popis: | 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-Mari\~no-Vafa conjecture, which reveals a deep relationship between Chern-Simons gauge theory and string theory, on torus links. Comment: 20 pages, 3 figures |
| Databáze: | OpenAIRE |
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