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Eigenvalues of products of unitary matrices and Lagrangian involutions. (English) Zbl 1081.58006

Summary: This paper introduces a submanifold of the moduli space of unitary representations of the fundamental group of a punctured sphere with fixed local monodromy. The submanifold is defined via products of involutions through Lagrangian subspaces. We show that the moduli space of Lagrangian representations is a Lagrangian submanifold of the moduli of unitary representations.

MSC:

58D19 Group actions and symmetry properties
53D12 Lagrangian submanifolds; Maslov index
58D27 Moduli problems for differential geometric structures
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