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.