A Note on Lagrangian Loci of Quotients

[摘要] We study Hamiltonian actions of compact groups in the presence ofcompatible involutions. We show that the Lagrangian fixed point seton the symplectically reduced space is isomorphic to the disjointunion of the involutively reduced spaces corresponding toinvolutions on the group strongly inner to the given one.Our techniques imply that the solution to the eigenvalues of a sum problemfor a given real form can be reduced to the quasi-split real form in thesame inner class. We also consider invariant quotients with respect tothe corresponding real form of the complexified group.

[学科分类] 数学（综合）

[关键词] Quotients;involutions;real forms;Lagrangian loci