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 |