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Abstract:
In this talk, we generalize to arbitrary surface groups and
arbitrary compact connected Lie groups the notion of decomposable
representation, first introduced by Falbel and Wentworth for unitary
representations of the punctured sphere group. We show that such
decomposable representations are the elements of the
fixed-point set of an anti-symplectic involution defined on the moduli
space of representations, forming therefore a Lagrangian submanifold
of this moduli space. The existence of decomposable representations is
obtained as a corollary of a real convexity theorem for group-valued
momentum maps.
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