报告题目：Cluster Nature of Quantum Groups

报告人：沈临辉，Michigan State University

时间：2022年10月28日（周五）10:00-11:00

Zoom: 878 457 4760

https://us04web.zoom.us/j/8784574760?pwd=cVg1b3lLTWRPVC9rRzhVODhNeitqQT09

密码：117673

摘要：By the applying the cluster theory of higher Teichmuller spaces, we present a rigid cluster model to realize the quantum group $U_q(g)$ for $g$ of type ADE. That is, we prove that there is a natural Hopf algebra isomorphism from the quantum group to a quotient algebra of the Weyl group invariants of a Fock-Goncharov quantum cluster algebra. By applying the quantum duality of cluster algebras, we show that the quantum group admits a cluster canonical basis $\Theta$ whose structural coefficients are in $\mathbb{N}[q^{\frac{1}{2}}, q^{-\frac{1}{2}}]$. The basis $\Theta$ satisfies an invariance property under Lusztig's braid group action, the Dynkin automorphisms, and the star anti-involution.

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