Abstract: This talk presents joint work with S. Fishel and I. Grojnowski on combinatorics arising from the socalled "flag variety" of a loop group. De Rham's theorem relates the holomorphic differentials on the flag variety to its topology; however, the variety being infinitedimensional, the connection is not quite as simple as in the finite dimensional compact case. The discrepancy gives rise to a hypergeometric summation formula of Ramanujan's (in the case of SL_{2}). Viewed from a different angle, our result affirms a conjecture of P. Hanlon's, which strengthened Macdonald's famous "constant term" formula. The relation between the two formulas involves the holomorphic Gbundles over the Riemann sphere.
