Quasi-Hamiltonian reduction via classical Chern-Simons theory
The author defines the shifted symplectic structures and Lagrangian morphisms and shows that by composing Lagrangian correspondences using pullbacks, one gets a composition in the category LagrCorr\(_n\). It is shown how the ordinary symplectic reduction and quasi-Hamiltonian reduction is adapted to shifted symplectic structures. Further, the correspondence between the operations in classical Chern-Simons theory and quasi-Hamiltonian reduction is explicitly given. Finally, a prequantization of the analytic character stack starting with a prequantization of the classifying stack BGL\(_n\) is provided.
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