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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Acknowledgments
The authors are grateful to Davide Gaiotto, Kevin Costello, and Li Yu for inspiring discussions. The first author was supported in part by the NSF grant DMS-1303462.
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Presented by: Valentin Ovsienko
To Alexander Alexandrovich Kirillov on his 80th Birthday.
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Ginzburg, V., Rozenblyum, N. Gaiotto’s Lagrangian Subvarieties via Derived Symplectic Geometry. Algebr Represent Theor 21, 1003–1015 (2018). https://doi.org/10.1007/s10468-018-9801-9
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DOI: https://doi.org/10.1007/s10468-018-9801-9