THE QUANTUM sl(n, C) REPRESENTATION THEORY AND ITS APPLICATIONS
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In this paper, we study the quantum sl(n) representation category using the web space. Specially, we extend sl(n) web space for n ≥4 as generalized Temperley-Lieb algebras. As an application of our study,we find that the HOMFLY polynomial Pn(q) specialized to a one variable polynomial can be computed by a linear expansion with respect to a presentation of the quantum representation category of sl(n). Moreover,we correct the false conjecture [30] given by Chbili, which addresses the relation between some link polynomials of a periodic link and its factor link such as Alexander polynomial (n = 0) and Jones polynomial (n = 2)and prove the corrected conjecture not only for HOMFLY polynomial but also for the colored HOMFLY polynomial specialized to a one variable polynomial.
Abstract
In this paper, we study the quantum sl(n) representation category using the web space. Specially, we extend sl(n) web space for n ≥4 as generalized Temperley-Lieb algebras. As an application of our study,we find that the HOMFLY polynomial Pn(q) specialized to a one variable polynomial can be computed by a linear expansion with respect to a presentation of the quantum representation category of sl(n). Moreover,we correct the false conjecture [30] given by Chbili, which addresses the relation between some link polynomials of a periodic link and its factor link such as Alexander polynomial (n = 0) and Jones polynomial (n = 2)and prove the corrected conjecture not only for HOMFLY polynomial but also for the colored HOMFLY polynomial specialized to a one variable polynomial.
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