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arXiv · 1601.02148

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

Yury A. Neretin
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Abstract

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.

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Yury A. Neretin. 2016-01-09. The group of diffeomorphisms of the circle: reproducing kernels and analogs of spherical functions. https://doi.org/10.3934/jgm.2017009

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