Non-commutative matrix integrals and representation varieties of surface groups in a finite group. (Q2574204)

From the authors' introduction: The purpose of this paper is to establish Feynman diagram expansion formulas for non-commutative matrix integrals over a finite-dimensional real or complex von Neumann algebra. An interesting case is the real or complex group algebra of a finite group. Using the graphical expansion formulas, we give a new proof of the classical formulas for the number of homomorphisms from the fundamental group of a closed surface into a finite group. Indeed, our integrals are generating functions for the cardinality of the representation variety of a surface group in a finite group.