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

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

In [7] it was shown that if n is the fundamental group ofa closed oriented surface S and G is Lie group satisfying very general conditions, then the space Hom(n, G)/G of conjugacy classes of representation n-+G has a natural symplectic structure. This symplectic structure generalizes the Weil-Petersson Kahler form on Teichmiiller space (taking G= PSL(2, lR)), the cup-product linear symplectic s...

INEXTENSIBLE FLOWS OF CURVES IN LIE GROUPS

In this paper, we study inextensible ows in three dimensional Lie groups with a bi-invariant metric. The necessary and sucient conditions for inextensible curve ow are expressed as a partial dierential equation involving the curvatures. Also, we give some results for special cases of Lie groups.

Translation-invariant Cones of Functions on Semi-simple Lie Groups

Introduction. Originally, the phrase harmonic analysis had a function-theoretic meaning, referring to the decomposition of a function into exponentials. In the current interpretation, particularly in connection with noncommutative groups, the term refers not to functions but to representations, and harmonic analysis is regarded as part of the theory of group representations. This shift in inter...

Invariant Smoothing on Lie Groups

In this paper we propose a (non-linear) smoothing algorithm for group-affine observation systems, a recently introduced class of estimation problems on Lie groups that bear a particular structure. As most non-linear smoothing methods, the proposed algorithm is based on a maximum a posteriori estimator, determined by optimization. But owing to the specific properties of the considered class of p...

Nonholonomic Flows on Lie Groups