Symplectic implosion and the Grothendieck-Springer resolution

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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.
Original languageEnglish
Pages (from-to) 767-792
Number of pages24
JournalTransformation Groups
Volume22
Early online date20 Jul 2016
DOIs
Publication statusPublished - 30 Sep 2017

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