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Transparent $SL_n$-skeins

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Speaker: 
Francis Bonahon
Affiliation: 
University of Southern California/Michigan state University
Date: 
Thu, 15/05/2025 - 11:30 - 12:30
Location: 
MPIM Lecture Hall

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 “transparency” property, in the sense that they can be traversed by any other skein without changing the resulting total skein. I will describe some (and conjecturally all) of these transparent 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.

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