The moduli stack M X (E 8 ) of principal E 8 -bundles over a smooth projective curve X carries a natural divisor ∆. We study the pull-back of the divisor ∆ to the moduli stack M X (P ), where P is a semi-simple and simply connected group such that its Lie algebra Lie(P ) is a maximal conformal subalgebra of Lie(E 8 ). We show that the divisor ∆ induces "Strange Duality"-type isomorphisms between the Verlinde spaces at level one of the following pairs of A similar isomorphism is obtained for the pair (Spin(8), Spin (8)) -see section 7.2.1. We would like to mention that the proofs of Theorem 1 and Theorem 2 are independent, and that both results are related by the fact that the "Strange Duality" isomorphism of Theorem 2 corresponding to the canonical M X (N)-linearization is obtained precisely by pulling-back the E 8 -theta divisor ∆ to the moduli stack M X (A × B).The last few years have seen important progress on "Strange Duality" or "rank-level" duality for Verlinde spaces. For a survey we refer, for example, to the papers [MO], [Po] or [Pa].We would like to thank Laurent Manivel and Nicolas Ressayre for helpful comments, as well as the referees for helping us improve readability of the paper.

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Using multiple Bernoulli series, we give a formula in the spirit of Euler-MacLaurin formula. We also give a wall crossing formula and a decomposition formula for multiple Bernoulli series. The study of these series is motivated by formulae of E. Witten for volumes of moduli spaces of flat bundles over a surface.

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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.