Papers › On the Hecke algebras and the colored HOMFLY polynomial
On the Hecke algebras and the colored HOMFLY polynomial
Xiao-Song Lin, Hao Zheng
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The colored HOMFLY polynomial is the quantum invariant of oriented links in S³ associated with irreducible representations of the quantum group U_q(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.
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