scholarly journals Complete families of commuting functions for coisotropic Hamiltonian actions

2019 ◽  
Vol 348 ◽  
pp. 523-540 ◽  
Author(s):  
Ernest B. Vinberg ◽  
Oksana S. Yakimova
Keyword(s):  
Hamiltonian Actions

scholarly journals Weakly Hamiltonian actions

2017 ◽  
Vol 115 ◽  
pp. 131-138
Author(s):  
David Martínez Torres ◽  
Eva Miranda
Keyword(s):  
Hamiltonian Actions

Rigidity of Hamiltonian Actions

2003 ◽  
Vol 46 (2) ◽  
pp. 277-290 ◽  
Author(s):  
Frédéric Rochon
Keyword(s):  
General Theory ◽  
Lie Group ◽  
Geometric Analysis ◽  
Smooth Action ◽  
Symplectic Action ◽  
Hamiltonian Actions

AbstractThis paper studies the following question: Given an ω′-symplectic action of a Lie group on a manifoldMwhich coincides, as a smooth action, with a Hamiltonian ω-action, when is this action a Hamiltonian ω′-action? Using a result of Morse-Bott theory presented in Section 2, we show in Section 3 of this paper that such an action is in fact a Hamiltonian ω′-action, provided thatM is compact and that the Lie group is compact and connected. This result was first proved by Lalonde-McDuff-Polterovich in 1999 as a consequence of a more general theory that made use of hard geometric analysis. In this paper, we prove it using classical methods only.

scholarly journals Rigidity of Hamiltonian actions on Poisson manifolds

2012 ◽  
Vol 229 (2) ◽  
pp. 1136-1179 ◽  
Author(s):  
Eva Miranda ◽  
Philippe Monnier ◽  
Nguyen Tien Zung
Keyword(s):  
Poisson Manifolds ◽  
Hamiltonian Actions

A global slice theorem for proper Hamiltonian actions

1999 ◽  
Vol 98 (3) ◽  
pp. 295-305
Author(s):  
Peter Heinzner ◽  
Frank Loose
Keyword(s):  
Slice Theorem ◽  
Hamiltonian Actions

scholarly journals A Note on Lagrangian Loci of Quotients

2005 ◽  
Vol 48 (4) ◽  
pp. 561-575 ◽  
Author(s):  
Philip Foth
Keyword(s):  
Fixed Point ◽  
Disjoint Union ◽  
Compact Groups ◽  
Real Form ◽  
Fixed Point Set ◽  
Point Set ◽  
Reduced Space ◽  
The Given ◽  
Hamiltonian Actions

AbstractWe 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.

scholarly journals Super loop groups, Hamiltonian actions and super Virasoro algebras

1990 ◽  
Vol 132 (2) ◽  
pp. 315-347 ◽  
Author(s):  
J. Harnad ◽  
B. A. Kupershmidt
Keyword(s):  
Loop Groups ◽  
Hamiltonian Actions
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