Non-commutative matrix integrals and representation varieties of surface groups in a finite group

Details Non-commutative matrix integrals and representation varieties of surface groups in a finite group Non-commutative matrix integrals and representation varieties of surface groups in a finite group

2002-11-07

arxiv.org/abs/math/0211127v3

Annales de l'Institut Fourier vol. 55, 1001--1036 (2005)

Mathematics

Quantum Algebra

27 pages, 10 figures

Scientific paper

A graphical expansion formula for non-commutative matrix integrals with values in a finite-dimensional real or complex von Neumann algebra is obtained in terms of ribbon graphs and their non-orientable counterpart called Moebius graphs. The contribution of each graph is an invariant of the topological type of the surface on which the graph is drawn. As an example, we calculate the integral on the group algebra of a finite group. We show that the integral is a generating function of the number of homomorphisms from the fundamental group of an arbitrary closed surface into the finite group. The graphical expansion formula yields a new proof of the classical theorems of Frobenius, Schur and Mednykh on these numbers.

Affiliated with

Also associated with

No associations

Rating

Non-commutative matrix integrals and representation varieties of surface groups in a finite group does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Non-commutative matrix integrals and representation varieties of surface groups in a finite group, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Non-commutative matrix integrals and representation varieties of surface groups in a finite group will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-407575