Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Maeda, Kazushi, Oshima, Yoshiki
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: リー群のユニタリ表現と等質空間上のD加群
OpenAlex ID: W7118857752
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