CARTAN DECOMPOSITION FOR COMPLEX LOOP GROUPS

Alexander Braverman; David Kazhdan

doi:10.1007/s00031-014-9268-7

CARTAN DECOMPOSITION FOR COMPLEX LOOP GROUPS

Alexander Braverman^*
, David Kazhdan

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

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 in [3], [6]. The main technical tool that we use is the (well-known) interpretation of twisted conjugacy classes in the holomorphic loop group in terms of principal holomorphic bundles on an elliptic curve.

Original language	English
Pages (from-to)	303-311
Number of pages	9
Journal	Transformation Groups
Volume	19
Issue number	2
DOIs	https://doi.org/10.1007/s00031-014-9268-7
State	Published - Jun 2014

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title = "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 in [3], [6]. The main technical tool that we use is the (well-known) interpretation of twisted conjugacy classes in the holomorphic loop group in terms of principal holomorphic bundles on an elliptic curve.",

author = "Alexander Braverman and David Kazhdan",

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AB - 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 in [3], [6]. The main technical tool that we use is the (well-known) interpretation of twisted conjugacy classes in the holomorphic loop group in terms of principal holomorphic bundles on an elliptic curve.

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CARTAN DECOMPOSITION FOR COMPLEX LOOP GROUPS

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