Quasi-parabolic Siegel Formula
Abstract
Description
The result of Siegel that the Tamagawa number of $SL_r$ over a function field is 1 has an expression purely in terms of vector bundles on a curve, which is known as the Siegel formula. We prove an analogous formula for vector bundles with quasi-parabolic structures. This formula can be used to calculate the Betti numbers of the moduli of parabolic vector bundles using the Weil conjucture.
LaTeX, 6 pages. Reason for re-submission : A factor that was missing in the first version is now included in the formula
LaTeX, 6 pages. Reason for re-submission : A factor that was missing in the first version is now included in the formula