SYMPLECTIC IMPLOSION AND THE GROTHENDIECK-SPRINGER RESOLUTION

SYMPLECTIC IMPLOSION AND THE GROTHENDIECK-SPRINGER RESOLUTION We prove that the Grothendieck-Springer simultaneous resolution viewed as a correspondence between the adjoint quotient of a Lie algebra and its maximal torus is Lagrangian in the sense of shifted symplectic structures. As Hamiltonian spaces can be interpreted as Lagrangians in the adjoint quotient, this allows one to reduce a Hamiltonian G-space to a Hamiltonian H-space where H is the maximal torus of G. We show that this procedure coincides with an algebraic version of symplectic implosion of Guillemin, Jeffrey and Sjamaar. We explain how to obtain generalizations of this picture to quasi-Hamiltonian spaces and their elliptic version. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Transformation Groups Springer Journals

SYMPLECTIC IMPLOSION AND THE GROTHENDIECK-SPRINGER RESOLUTION

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Publisher
Springer US
Copyright
Copyright © 2016 by The Author(s)
Subject
Mathematics; Topological Groups, Lie Groups; Algebra
ISSN
1083-4362
eISSN
1531-586X
D.O.I.
10.1007/s00031-016-9398-1
Publisher site
See Article on Publisher Site

Abstract

We prove that the Grothendieck-Springer simultaneous resolution viewed as a correspondence between the adjoint quotient of a Lie algebra and its maximal torus is Lagrangian in the sense of shifted symplectic structures. As Hamiltonian spaces can be interpreted as Lagrangians in the adjoint quotient, this allows one to reduce a Hamiltonian G-space to a Hamiltonian H-space where H is the maximal torus of G. We show that this procedure coincides with an algebraic version of symplectic implosion of Guillemin, Jeffrey and Sjamaar. We explain how to obtain generalizations of this picture to quasi-Hamiltonian spaces and their elliptic version.

Journal

Transformation GroupsSpringer Journals

Published: Jul 20, 2016

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