Videos

Skein identities at roots of unity

Presenter
December 11, 2025
Abstract
The Kauffman bracket skein algebra of an oriented surface is built from knots labeled by representations of Uq(sl2). When q is generic, the irreducible representations of Uq(sl2) correspond to the Jones-Wenzl projectors from the Temperley-Lieb category. When q is a root of unity, the relationship between the TL category and Uq(sl2)-mod is less complete but is combinatorially richer. We will discuss special skein identities involving Jones-Wenzl projectors at roots of unity. We will discuss how the easiest such identity can be used to recover the Chebyshev-Frobenius homomorphism of Bonahon-Wong. This is joint work with Indraneel Tambe.
Supplementary Materials