A Note on Lagrangian Loci of Quotients
Printed: Dec 2005
We study Hamiltonian actions of compact groups in the presence of
compatible involutions. We show that the Lagrangian fixed point set
on the symplectically reduced space is isomorphic to the disjoint
union of the involutively reduced spaces corresponding to
involutions on the group strongly inner to the given one.
Our techniques imply that the solution to the eigenvalues of a sum problem
for a given real form can be reduced to the quasi-split real form in the
same inner class. We also consider invariant quotients with respect to
the corresponding real form of the complexified group.
Quotients, involutions, real forms, Lagrangian loci
53D20 - Momentum maps; symplectic reduction