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Symplectic implosion and the Grothendieck-Springer resolution

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 ...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Publisher's Version

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Publisher copy:
10.1007/s00031-016-9398-1

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Department:
Oxford, MPLS, Mathematical Institute
Role:
Author
Publisher:
Springer Verlag
Journal:
Transformation Groups Journal website
Publication date:
2016-07-20
Acceptance date:
2016-04-27
DOI:
EISSN:
1531-586X
ISSN:
1083-4362
Pubs id:
pubs:511460
URN:
uri:639307b1-897d-4410-b667-ef602ef217d2
UUID:
639307b1-897d-4410-b667-ef602ef217d2
Local pid:
pubs:511460

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