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arXiv · 2609.26630

Multiplicity One Property for Archimedean Theta Correspondence

Zhibin Geng·Kaidi Wu
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Abstract

For any archimedean reductive dual pair, we prove that the Jordan-Hölder multiplicity of the small theta lift in the full theta lift is one. The main input is an equality between the multiplicities of the lowest degree $K$-types in the full and small theta lifts. We also deduce a new description of the archimedean theta correspondence in terms of lowest degree K-types.

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Zhibin Geng, Kaidi Wu. 2026-09-22. Multiplicity One Property for Archimedean Theta Correspondence. https://arxiv.org/abs/2609.26630

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