The group of diffeomorphisms of the circle: reproducing kernels and analogs of spherical functions

The group \(Diff\) of diffeomorphisms of the circle is an infinite dimensional analog of the real semisimple Lie groups \(U(p,q)\), \(Sp(2n,R)\), \(SO^*(2n)\); the space \(\Xi\) of univalent functions is an analog of the corresponding classical complex Cartan domains. We present explicit formulas fo...

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Bibliographic Details
Published in:	arXiv.org
Main Author:	Neretin, Yury A
Format:	Paper
Language:	English
Published:	Ithaca Cornell University Library, arXiv.org 09.01.2016
Subjects:	Domains Isomorphism Kernels Lie groups Weight
ISSN:	2331-8422
Online Access:	Get full text
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Summary:	The group \(Diff\) of diffeomorphisms of the circle is an infinite dimensional analog of the real semisimple Lie groups \(U(p,q)\), \(Sp(2n,R)\), \(SO^*(2n)\); the space \(\Xi\) of univalent functions is an analog of the corresponding classical complex Cartan domains. We present explicit formulas for realizations of highest weight representations of \(Diff\) in the space of holomorphic functionals on \(\Xi\), reproducing kernels on \(\Xi\) determining inner products, and expressions ('canonical cocycles') replacing spherical functions.
Bibliography:	SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50
ISSN:	2331-8422
DOI:	10.48550/arxiv.1601.02148