PGL2 webs at roots of unity
Vijay Higgins, Bryan Silva, Amy Somers, David Stephens, Srijan Sundar, Parth Wokhlu
Abstract
We study webs on surfaces for the PGL2 skein theory specialized at roots of unity. We construct the PGL2 analogue of Chebyshev polynomials and use them to construct central elements in the skein algebra. We then focus on the cases of the 3-punctured sphere and the closed torus. We compute the Frobenius homomorphism for these two surfaces and show that the PGL2 Frobenius homomorphism for the torus is not injective when the quantum parameter q2 is a root of unity of even order n.
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