Learning Seminar 10/13

Speaker: Yutong Li

Abstract: We introduce an explicit formula for the two-variable HOMFLY(PT) polynomial based on a trace on the Hecke algebra H_n(q) due to Ocneanu. In particular, this trace could be computed as a sum over Young diagrams corresponding to partitions of n. Then, we will focus on the case of torus knots, where the formula simplifies significantly. Finally, we establish the connection between coefficients of the HOMFLY polynomial of torus knots and q-analogs of Catalan numbers.

References:

• https://www.jstor.org/stable/1971403

• Section 3.1 of https://arxiv.org/pdf/1003.0916.pdf