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| Auteurs principaux: | , |
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| Format: | Preprint |
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2026
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| Accès en ligne: | https://arxiv.org/abs/2601.02188 |
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| _version_ | 1866915710751473664 |
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| author | Maeda, Kazushi Oshima, Yoshiki |
| author_facet | Maeda, Kazushi Oshima, Yoshiki |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_02188 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Square integrability of regular representations on reductive homogeneous spaces Maeda, Kazushi Oshima, Yoshiki Representation Theory 22E46 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. |
| title | Square integrability of regular representations on reductive homogeneous spaces |
| topic | Representation Theory 22E46 |
| url | https://arxiv.org/abs/2601.02188 |