The moment map for a multiplicity free action

Authors:
Chal Benson, Joe Jenkins, Ronald L. Lipsman and Gail Ratcliff

Journal:
Bull. Amer. Math. Soc. **31** (1994), 185-190

MSC:
Primary 22C05; Secondary 22E30

MathSciNet review:
1260517

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Abstract: Let *K* be a compact connected Lie group acting unitarily on a finite-dimensional complex vector space *V*. One calls this a *multiplicity-free* action whenever the *K*-isotypic components of are *K*-irreducible. We have shown that this is the case if and only if the moment map for the action is finite-to-one on *K*-orbits. This is equivalent to a result concerning Gelfand pairs associated with Heisenberg groups that is motivated by the Orbit Method. Further details of this work will be published elsewhere.

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Additional Information

DOI:
https://doi.org/10.1090/S0273-0979-1994-00514-2

Keywords:
Gelfand pairs,
Heisenberg group,
Orbit Method,
moment map

Article copyright:
© Copyright 1994
American Mathematical Society