Multiple Bernoulli series and volumes of moduli spaces of flat bundles over surfaces

Abstract

Using Szenes formula for multiple Bernoulli series we explain how to compute Witten series associated to classical Lie algebras. Particular instances of these series compute volumes of moduli spaces of flat bundles over surfaces, and also certain multiple zeta values.

arXiv comment51 pages, 3 figures; formula in Proposition 3.1 for the Lie group of type G_2 is corrected; new references added