The $L_p$-dual space of a semisimple Lie group
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916254702370816 |
|---|---|
| author | Bekka, Bachir |
| author_facet | Bekka, Bachir |
| contents | Let $G$ be a semisimple Lie group. We describe the irreducible representations of $G$ by linear isometries on $L_p$-spaces for $p\in (1,+\infty)$ with $p\neq 2.$ More precisely, we show that, for every such representation $π,$ there exists a parabolic subgroup $Q$ of $G$ such that $π$ is equivalent to the natural representation of $G$ on $L_p(G/Q)$ twisted by a unitary character of $Q.$ When $G$ is of real rank one, we give a complete classification of the possible irreducible representations of $G$ on an $L_p$-space for $p\neq 2,$ up to equivalence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_12919 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The $L_p$-dual space of a semisimple Lie group Bekka, Bachir Representation Theory Dynamical Systems Operator Algebras 22E46, 47L10, 37A40 Let $G$ be a semisimple Lie group. We describe the irreducible representations of $G$ by linear isometries on $L_p$-spaces for $p\in (1,+\infty)$ with $p\neq 2.$ More precisely, we show that, for every such representation $π,$ there exists a parabolic subgroup $Q$ of $G$ such that $π$ is equivalent to the natural representation of $G$ on $L_p(G/Q)$ twisted by a unitary character of $Q.$ When $G$ is of real rank one, we give a complete classification of the possible irreducible representations of $G$ on an $L_p$-space for $p\neq 2,$ up to equivalence. |
| title | The $L_p$-dual space of a semisimple Lie group |
| topic | Representation Theory Dynamical Systems Operator Algebras 22E46, 47L10, 37A40 |
| url | https://arxiv.org/abs/2405.12919 |