The elliptic curve in the S-duality theory and Eisenstein series for Kac-Moody groups
| dc.creator | Kapranov, M. | |
| dc.date | 2000-01-02 | |
| dc.date | 2000-02-21 | |
| dc.date.accessioned | 2026-07-07T04:33:10Z | |
| dc.date.available | 2026-07-07T04:33:10Z | |
| dc.description | We establish a relation between the generating functions appearing in the S-duality conjecture of Vafa and Witten and geometric Eisenstein series for Kac-Moody groups. For a pair consisting of a surface and a curve on it, we consider a refined geometric function E (involving G-bundles with parabolic structures along the curve) which depends both on elliptic and modular variables. We prove a functional equation for E with respect to the affine Weyl group, thus establishing the elliptic behavior. When the curve is P^1, we calculate the Eisenstein-Kac-Moody series explicitly and it turns out to be a certain deformation of an irreducible Kac-Moody character, more precisely, an analog of the Hall-Littlewood polynomial for the affine root system. We also get an explicit formula for the universal blowup function for any simply connected structure group. | |
| dc.description | 41 pages, AMS-Tex. Substantially revised and expanded version | |
| dc.identifier | https://arxiv.org/abs/math/0001005 | |
| dc.identifier | http://arxiv.org/abs/math/0001005 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58475 | |
| dc.subject | Algebraic Geometry | |
| dc.title | The elliptic curve in the S-duality theory and Eisenstein series for Kac-Moody groups | |
| dc.type | text |