Description
Spin graph functions of Reshetikhin-Stokman are generalizations of vector-valued spherical functions that arise in many contexts in harmonic analysis and physics. In this talk I will consider a special class of spin graph functions for the (identity connected component of the) Lorentz group SO$(n,1)_e$, which is relevant for the analysis of Euclidean four-point local correlation functions in $(n-1)$-dimensional conformal field theory. I will present a construction, mapping such smooth spin graph functions to smooth vector-valued functions on a certain Cartan subgroup of the Lorentz group, and discuss the pushforward under that map of the algebra of invariant differential operators acting on the spin graph functions. This in particular provides an explicit representation of the corresponding algebra of quantum Hamiltonians by endomorphism-valued differential operators. The talk is based on the joint work with Edward Berengoltz and Jasper Stokman.