Three Theorems on the 6j Symbol of the Modular Double of Uq(sl2(R))

Explore three fundamental theorems concerning the 6j symbol of the modular double of Uq(sl2(R)) in this mathematical lecture delivered by Xin Sun from Peking University. Delve into advanced concepts at the intersection of quantum algebra, representation theory, and mathematical physics as part of a conference on Topological Recursion, Conformal Field Theory, and Random Geometry. Examine the mathematical structures and properties of 6j symbols within the framework of quantum groups, specifically focusing on the modular double construction of the quantum deformation of sl2(R). Gain insights into the theoretical foundations and applications of these symbols in modern mathematical physics, including their connections to conformal field theory and topological recursion methods.