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arXiv · 2204.00243

Cartan Motion Group and Orbital Integrals

Yanli Song·Xiang Tang
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Abstract

In this short note, we study the variation of orbital integrals, as traces on the group algebra $G$, under the deformation groupoid. We show that orbital integrals are continuous under the deformation. And we prove that the pairing between orbital integrals and $K$-theory element of $C^*_r(G)$ stays constant with respect to the deformation for regular group elements, but vary at singular elements.

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Yanli Song, Xiang Tang. 2022-04-01. Cartan Motion Group and Orbital Integrals. https://arxiv.org/abs/2204.00243

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