Cartan decomposition for complex loop groups
Abstract
In this note we formulate and prove a version of Cartan decomposition for holomorphic loop groups, similar to Cartan decomposition for $p$adic loop groups, discussed proved by Garland (and later by the authors by geometric mathods). The main technical tool that we use is the (wellknown) interpretation of twisted conjugacy classes in the holomorphic loop group in terms of principal holomorphic bundles on an elliptic curve.
 Publication:

arXiv eprints
 Pub Date:
 February 2014
 arXiv:
 arXiv:1402.1369
 Bibcode:
 2014arXiv1402.1369B
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  Algebraic Geometry
 EPrint:
 8 pages