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In this paper, we construct a Lagrangian submanifold of the moduli spaceassociated to the fundamental group of a punctured Riemann surface (the spaceof representations of this fundamental group into a compact connected Liegroup). This Lagrangian submanifold is obtained as the fixed-point set of ananti-symplectic involution defined on the moduli space. The notion ofdecomposable representation provides a geometric interpretation of thisLagrangian submanifold

Decomposable representations and Lagrangian submanifolds of moduli spaces associated to surface groups