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A Note on Lagrangian Loci of Quotients

Published online by Cambridge University Press:  20 November 2018

Philip Foth
Philip Foth*
Affiliation:
Department of Mathematics, University of Arizona, Tucson, AZ 85721-0089 e-mail: foth@math.arizona.edu
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Abstract

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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.

Keywords

53D20Quotientsinvolutionsreal formsLagrangian loci
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 48 , Issue 4 , 01 December 2005 , pp. 561 - 575
Copyright
Copyright © Canadian Mathematical Society 2005

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