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Geometry and Physics Seminar

Symmetries of Hamiltonian actions of reductive groups and of supersymmetric gauge theories

David Ben-Zvi, UT Austin

Location:  Serin E372
Date & time: Thursday, 01 March 2018 at 1:00PM - 2:00PM

Title: Symmetries of Hamiltonian actions of reductive groups and of supersymmetric gauge theories

 

Abstract: Classical and quantum Hamiltonian actions of reductive groups, respectively, 

give rise to ubiquitous families of commuting flows and of commutative rings of operators. I will explain how a construction independently due to Knop and NgĂ´ (from the proof of the Fundamental Lemma) provides a universal integration of these flows for classical systems. I will then explain, following joint work with Sam Gunningham, how to quantize this action to obtain universal symmetries of the corresponding quantum systems. The action can be understood as a symmetry in supersymmetric gauge theories which is a nonabelian generalization of the invariance of Maxwell theory under shifts of the electromagnetic potential.

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Department of Mathematics

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Rutgers University
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