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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2601.03049 |
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| _version_ | 1866917187187376128 |
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| author | Maeda, Kazushi |
| author_facet | Maeda, Kazushi |
| 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 $G$. They introduced the functions $ρ$ on Lie algebras and gave a necessary and sufficient condition for the temperedness of $L^2(G/H)$ in terms of an inequality on $ρ$. In a joint work with Y. Oshima, we considered when $L^2(G/H)$ is equivalent to a unitary subrepresentation of $L^2(G)$ and gave a sufficient condition for this in terms of a strict inequality of $ρ$. In this paper, we will classify the pairs $(\mathfrak{g}, \mathfrak{h})$ with $\mathfrak{g}$ complex reductive and $\mathfrak{h}$ complex semisimple which satisfy that strict inequality of $ρ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_03049 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Classification of reductive homogeneous spaces satisfying strict inequality for Benoist-Kobayashi's $ρ$ functions Maeda, Kazushi Representation Theory 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 $G$. They introduced the functions $ρ$ on Lie algebras and gave a necessary and sufficient condition for the temperedness of $L^2(G/H)$ in terms of an inequality on $ρ$. In a joint work with Y. Oshima, we considered when $L^2(G/H)$ is equivalent to a unitary subrepresentation of $L^2(G)$ and gave a sufficient condition for this in terms of a strict inequality of $ρ$. In this paper, we will classify the pairs $(\mathfrak{g}, \mathfrak{h})$ with $\mathfrak{g}$ complex reductive and $\mathfrak{h}$ complex semisimple which satisfy that strict inequality of $ρ$. |
| title | Classification of reductive homogeneous spaces satisfying strict inequality for Benoist-Kobayashi's $ρ$ functions |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2601.03049 |