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arXiv · 2407.03366

Spherical Distributions on the De Sitter Space and their Spectral Singularities

Iswarya Sitiraju
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Abstract

A spherical distribution is an eigendistribution of the Laplace-Beltrami operator with certain invariance on the de Sitter space. Let G'=O(1,n;R) be the Lorentz group and H' = O(1,n-1;R) be its subgroup. The authors Olafsson and Sitiraju have constructed the spherical distributions, which are $H'$-invariant, as boundary values of some sesquiholomorphic kernels. In this survey article we will explore the connections of these kernels with reflection positivity and representations of the group G = SO(1,n;R)_e, which is the connected component of the Lorentz group. We will also discuss the singularities of spherical distributions in terms of their wavefront set.

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Iswarya Sitiraju. 2024-06-29. Spherical Distributions on the De Sitter Space and their Spectral Singularities. https://arxiv.org/abs/2407.03366

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