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FIELD
Mathematics
DATE
Dec 23 (Tue), 2025
TIME
14:30 ~ 16:00
PLACE
1423
SPEAKER
Higgins, Vijay
HOST
Kim, Hyun Kyu
INSTITUTE
UCLA
TITLE
[Geom., Alg. & Phys.] Skein identities at roots of unity
ABSTRACT
The Kauffman bracket relations give a simple topological description of the representation category of the quantum group associated to sl(2), denoted by Uq(sl2). One can use the relations to build the skein algebra of an oriented surface by labeling components of knot diagrams on the surface 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) representation category is less complete, but it 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. (https://sites.google.com/view/gapkias) (also will be broadcast by Zoom: Meeting ID 881 6733 5502, passwd 702101, link https://kias-re-kr.zoom.us/j/88167335502?pwd=bZnuHJASb0zVetBMxXTLbORee330K1.1)
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