The tail of the one-row colored sl(3) Jones polynomial and the Andrews-Gordon type identity

2020/07/09 Thu 10:30 - 12:00
Wataru Yuasa
RIMS, Kyoto University

I will review my works on the one-row colored sl(3) tail of knots and links. The tail is a q-series obtained as a limit of the colored Jones polynomial. The first topic is the existence of tails of the one-row colored sl(3) colored Jones polynomials for oriented "adequate" links. In the case of sl(2), it showed by Armond and Garoufalidis-Le independently. The second topic is the Andrews-Gordon type identities for (false) theta series obtained from the tail of (2,m)-torus knots and links. It is known that our formula of one-row colored sl(3) tail coincides with the diagonal part of the sl(3) false theta function obtained by Bringmann-Kaszian-Milas.In this talk, I will also give a quick review on quantum invariants of knots and links.

(This seminar was held on zoom.)