Cluster Nature of Quantum Groups
Explore the cluster nature of quantum groups in this M-Seminar talk from Kansas State University. Delve into a rigid cluster model that realizes the quantum group U_q(g) for g of type ADE. Discover how a natural Hopf algebra isomorphism connects the quantum group to a quotient algebra of Weyl group invariants in a Fock-Goncharov quantum cluster algebra. Learn about the application of quantum duality in cluster algebras, revealing that the quantum group possesses a cluster canonical basis Θ with structural coefficients in N[q^(1/2), q^(-1/2)]. Examine the invariance properties of basis Θ under braid group action, Dynkin automorphisms, and star anti-involution. Based on the preprint arXiv: 2209.06258, this hour-long lecture by Linhui Shen from Michigan State University offers an in-depth exploration of advanced concepts in quantum algebra and representation theory.