Abstract. We study the ring generated by the Chern classes of tautological line bundles on the moduli space of parabolic bundles of arbitrary rank on a Riemann surface. We show the Poincaré duals to these Chern classes have simple geometric representatives. We use this construction to show that the ring generated by these Chern classes vanishes below the dimension of the moduli space, in analogy with the Newstead-Ramanan conjecture for stable bundles.

Let K ⊂ G be compact connected Lie groups with common maximal torus T . Let (M, ω) be a prequantisable compact connected symplectic manifold with a Hamiltonian G-action. Geometric quantisation gives a virtual representation of G; we give a formula for the character χ of this virtual representation as a quotient of virtual characters of K. When M is a generic coadjoint orbit our formula agrees with the Gross-Kostant-Ramond-Sternberg formula. We then derive a generalisation of the Guillemin-Prato multiplicity formula which, for λ a dominant integral weight of K, gives the multiplicity in χ of the irreducible representation of K of highest weight λ.

No abstract

We consider the moduli space of flat (2 + 1)-connections (up to gauge transformations) on a Riemann surface, with fixed holonomy around a marked point. There are natural line bundles over this moduli space; we construct geometric representatives for the Chern classes of these line bundles, and prove that the ring generated by these Chern classes vanishes below the dimension of the moduli space, generalizing a conjecture of Newstead.This article is part of the theme issue 'Finite dimensional integrable systems: new trends and methods'.

No abstract