Square integrability of regular representations on reductive homogeneous spaces

Kazushi Maeda; Yoshiki Oshima

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arXiv · 2601.02188

Square integrability of regular representations on reductive homogeneous spaces

Kazushi Maeda·Yoshiki Oshima

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Abstract

Let $G$ be a real reductive Lie group and $H$ a reductive subgroup of $G$. Benoist-Kobayashi studied when $L^2(G/H)$ is a tempered representation of $G$ and in particular they gave a necessary and sufficient condition for the temperedness in terms of certain functions on Lie algebras. In this paper, we consider when $L^2(G/H)$ is equivalent to a unitary subrepresentation of $L^2(G)$ and we will give a sufficient condition for this in terms of functions introduced by Benoist-Kobayashi. As a corollary, we prove the non-existence of discrete series for homogeneous spaces $G/H$ satisfying certain conditions.

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BibTeX RIS

Kazushi Maeda, Yoshiki Oshima. 2026-01-06. Square integrability of regular representations on reductive homogeneous spaces. https://arxiv.org/abs/2601.02188

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