Invisible SL_n-skeins
Organizers
Speaker
Francis Bonahon
Time
Wednesday, October 23, 2024 9:00 AM - 10:30 AM
Venue
A3-3-301
Online
Zoom 242 742 6089
(BIMSA)
Abstract
For a Lie group G, the G-skein module of a 3-dimensional manifold M is a fundamental object in Witten’s interpretation of quantum knot invariants in the framework of a topological quantum field theory. It depends on a parameter q and, when this parameter q is a root of unity, the G-skein module contains elements with a surprising “invisibility” property, in the sense that they can be traversed by any other skein without changing the resulting total skein. I will describe some of these invisible elements in the case of the special linear group SL_n. The construction is based on the very classical theory of symmetric polynomials in n variables.