Loop groups and diffeomorphism groups of the circle as colimits

2017/06/26 by Henriques, Andre · 1 citation
#22E67 #57S05 #FOS: Mathematics #FOS: Physical sciences #Group Theory (math.GR) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1706.08471

Abstract

We show that loop groups and the universal cover of Diff₊(S¹) can be expressed as colimits of groups of loops/diffeomorphisms supported in subintervals of S¹. Analogous results hold for based loop groups and for the based diffeomorphism group of S¹. These results continue to hold for the corresponding centrally extended groups. We use the above results to construct a comparison functor from the representations of a loop group conformal net to the representations of the corresponding affine Lie algebra. We also establish an equivalence of categories between solitonic representations of the loop group conformal net, and locally normal representations of the based loop group.

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• Representations of conformal nets associated with infinite-dimensional groups

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