The index formula for the moduli of $G$-bundles on a curve


We prove the formulae conjectured by the first author for the index of $K$-theory classes over the moduli stack of algebraic $G$-bundles on a smooth projective curve. The formulae generalize E. Verlinde’s for line bundles and have Witten’s integrals over the moduli space of stable bundles as their large level limits. As an application, we prove the Newstead-Ramanan conjecture on the vanishing of high Chern classes of certain moduli spaces of semi-stable $G$-bundles.


Constantin Teleman

Department of Mathematics
University of California
970 Evans Hall #3840
Berkeley, CA 94720-3840
United States

Christopher T. Woodward

Department of Mathematics
Rutgers University
110 Frelinghuysen Rd.
Piscataway, NJ 08854-8019
United States