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Abstract: This talk presents joint work with S. Fishel and I. Grojnowski on combinatorics arising from the so-called "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 infinite-dimensional, 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 SL2). 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 G-bundles over the Riemann sphere.
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