摘要
In [AB], Atiyah and Bott studied Yang-Mills functional over a Riemann surface from the point of view of Morse theory. In [HL4], we study Yang-Mills functional on the space of connections on a principal GR-bundle over a closed, connected, nonorientable surface, where GR is any compact connected Lie group. In this paper, we generalize the discussion in [AB] and [HL4]. We obtain explicit descriptions of equivariant Morse stratification of Yang-Mills functional on orientable and nonorientable surfaces for non-unitary classical groups SO(n) and Sp(n). When the surface is orientable, we use Laumon and Rapoport’s method [LR] to invert the Atiyah-Bott recursion relation, and write down explicit formulas of rational equivariant Poincar´e series of the semistable stratum of the space of holomorphic structures on a principal SO(n, C)-bundle or a principal Sp(n, C)-bundle.