Invariant functions on Lie groups and Hamiltonian flows of surface group representations (Q1089654)

In a previous paper [Adv. Math. 54, 200--225 (1984; Zbl 0574.32032)], the author has shown that if \(\pi\) is the fundamental group of a closed oriented surface \(S\) and \(G\) is a Lie group satisfying very general conditions, then the space \(\Hom(\pi,G)/G\) of conjugacy classes of representations \(\pi\to G\) has a natural symplectic structure. (This structure generalizes the Weil-Petersson Kähler form on Teichmüller spaces, the Kähler form on Jacobi varieties of Riemann surfaces homeomorphic to \(S\) and other well-known symplectic structures.) The purpose of this paper is to investigate the geometry of this symplectic structure with the aid of a natural family of functions on \(\Hom(\pi,G)/G\).