Transactions of the American Mathematical Society

Author(s): Xiao-Song Lin; Hao Zheng
Journal: Trans. Amer. Math. Soc. 362 (2010), 1-18.
MSC (2000): Primary 57M27, 20C08
Posted: July 31, 2009
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Abstract: The colored HOMFLY polynomial is the quantum invariant of oriented links in

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 the 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.

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Xiao-Song Lin
Affiliation: Department of Mathematics, University of California, Riverside, California 92521

Hao Zheng
Affiliation: Department of Mathematics, Zhongshan University, Guangzhou, Guangdong 510275, People's Republic of China
Email: zhenghao@mail.sysu.edu.cn

DOI: 10.1090/S0002-9947-09-04691-1
PII: S 0002-9947(09)04691-1
Received by editor(s): August 4, 2006
Posted: July 31, 2009
Additional Notes: The first author was supported in part by NSF grants DMS-0404511
The second author was supported in part by an NSFC grant
Copyright of article: Copyright 2009, American Mathematical Society

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