The University of Michigan Combinatorics Seminar
Winter 2001
January 26, 4:10-5:00, 4088 East Hall

Affine analogs of Hall polynomials and S-duality generating functions

Mikhail Kapranov

University of Toronto


Hall polynomials are certain deformations of the irreducible characters of a semisimple algebraic group. One can extend their definition to the case of affine root systems, getting some analytic functions (no longer polynomials). It turns out that these functions have an algebro-geometric interpretation, as certain generating functions of Hodge polynomials of the moduli spaces of G-bundles on ruled algebraic surfaces. The talk will explain this interpretation as well as the analogy between affine Hall "polynomials" and Eisenstein series.