October 13, 2025Open Access

Heat kernel, large-time behavior, and representation theory

Key Points

The study shows the large-time behavior of the G-trace, connecting it with representation theory.
An asymptotic formula was derived, which aligns with results from Vogan's minimal K-type theory.
Geometric aspects of symmetric spaces were examined in relation to the heat operator.
Carmona's proof of Vogan's lambda map supports the findings presented here.

Abstract

Given a real reductive group G, the purpose of this paper is to show an asymptotic formula of the large-time behavior of the G-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 K-type theory.

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Cite This Study

Shen et al. (Sat,) studied this question.

synapsesocial.com/papers/68ecc715d1cc7436f7d18ac8 https://doi.org/https://doi.org/10.48550/arxiv.2503.00554

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