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1 results

  • A Note on Lagrangian Loci of Quotients

  • Philip Foth
  • Journal:
    Canadian Mathematical Bulletin / Volume 48 / Issue 4 / 01 December 2005
    Published online by Cambridge University Press:
    20 November 2018, pp. 561-575
    Print publication:
    01 December 2005
    • Article
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  • 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.