Loop groups and diffeomorphism groups of the circle as colimits

Author: 

Henriques, A

Publication Date: 

6 March 2019

Journal: 

Communications in Mathematical Physics

Last Updated: 

2020-08-27T05:23:37.683+01:00

Issue: 

2

Volume: 

366

DOI: 

10.1007/s00220-019-03394-8

page: 

537-565

abstract: 

In this paper, we show that loop groups and the universal cover of Diff +(S 1) canbe 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.

Symplectic id: 

965587

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article