The duality paradigm for compact Lie groups, past and present
The duality paradigm for compact Lie groups, past and present
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Akshay Venkatesh, IAS & Princeton
It is a remarkable and nontrivial fact that there is a duality on the set of compact connected Lie groups; this interchanges,听for example, the group of 2x2 unitary matrices of determinant 1, and the group of rotations in three real dimensions.听This duality emerged in mathematics in the 1960s ("Langlands duality"), and independently in physics in the 1970s ("electric-magnetic duality").听听听 I will give a gentle introduction to this duality,听without assuming background in Lie theory, and say a few sketchy words about the role it plays in various settings.听 I will then say a little about听 my recent work with Ben-Zvi and Sakellaridis where we seek听听to incorporate into the duality spaces upon which the groups act.听