The heat kernel on $SL(2,\mathbb{R})$

Shota Mori

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arXiv · 1909.03670

The heat kernel on $SL(2,\mathbb{R})$

Shota Mori

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Abstract

Let $G$ be a noncompact semisimple Lie group equipped with a certain invariant Riemannian metric. Then, we can consider a heat kernel function on $G$ associated to the Riemannian metric. We give an explicit formula for the heat kernel when $G = SL(2,\mathbb{R})$. The main tools are spherical transform and Helgason-Fourier transform for homogeneous vector bundles studied by R. Camporesi.

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Shota Mori. 2019-09-09. The heat kernel on $SL(2,\mathbb{R})$. https://arxiv.org/abs/1909.03670

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