Heat kernel, large-time behavior, and representation theory
Differential Geometry
2025-05-27 v2 Representation Theory
Abstract
Given a real reductive group , the purpose of this paper is to show an asymptotic formula of the large-time behavior of the -trace of the heat operator on the associated symmetric spaces. Together with Carmona's proof on Vogan's lambda map, our results provide a geometric counterpart of Vogan's minimal -type theory.
Cite
@article{arxiv.2503.00554,
title = {Heat kernel, large-time behavior, and representation theory},
author = {Shu Shen and Yanli Song and Xiang Tang},
journal= {arXiv preprint arXiv:2503.00554},
year = {2025}
}
Comments
50 pages; the computation of the Novikov-Shubin type invariant for smooth locally symmetric spaces is added