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Gaiotto’s Lagrangian Subvarieties via Derived Symplectic Geometry

Authors
  • Ginzburg, Victor1
  • Rozenblyum, Nick1
  • 1 University of Chicago, Department of Mathematics, Chicago, IL, 60637, USA , Chicago (United States)
Type
Published Article
Journal
Algebras and Representation Theory
Publisher
Springer Netherlands
Publication Date
May 31, 2018
Volume
21
Issue
5
Pages
1003–1015
Identifiers
DOI: 10.1007/s10468-018-9801-9
Source
Springer Nature
Keywords
License
Yellow

Abstract

Let BunG be the moduli space of G-bundles on a smooth complex projective curve. Motivated by a study of boundary conditions in mirror symmetry, Gaiotto (2016) associated to any symplectic representation of G a Lagrangian subvariety of T∗BunG. We give a simple interpretation of (a generalization of) Gaiotto’s construction in terms of derived symplectic geometry. This allows to consider a more general setting where symplectic G-representations are replaced by arbitrary symplectic manifolds equipped with a Hamiltonian G-action and with an action of the multiplicative group that rescales the symplectic form with positive weight.

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