Stability Of The Parabolic Poincaré Bundle

Abstract

Given a compact Riemann surface $X$ and a moduli space $M_{\alpha }(\Lambda )$ of parabolic stable bundles on it of fixed determinant of complete parabolic flags, we prove that the Poincaré parabolic bundle on $X\times M_{\alpha }(\Lambda )$ is parabolic stable with respect to a natural polarization on $X\times M_{\alpha }(\Lambda )$.

To appear in International Journal of Geometric Methods in Modern Physics