Geodesic
Infinite dimensional representations of orthogonal groups of quadratic forms with finite index
Duchesne, Bruno1
1 Institut Élie Cartan, UMR 7502, Université de Lorraine et CNRS, Nancy, France
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 32 (2023) no. 2, pp. 371-396

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We study representations G→H where G is either a simple Lie group with real rank at least 2 or an infinite dimensional orthogonal group of some quadratic form of finite index at least 2 and H is such an orthogonal group as well. The real, complex and quaternionic cases are considered. Contrarily to the rank one case, we show that there is no exotic such representations and we classify these representations.

On the way, we make a detour and prove that the projective orthogonal groups PO K (p,∞) or their orthochronous component (where K denotes the real, complex or quaternionic numbers) are Polish groups that are topologically simple but not abstractly simple.

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DOI : 10.5802/afst.1740

Duchesne, Bruno 1

1 Institut Élie Cartan, UMR 7502, Université de Lorraine et CNRS, Nancy, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Infinite dimensional representations of orthogonal groups of quadratic forms with finite index},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {371--396},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
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Duchesne, Bruno. Infinite dimensional representations of orthogonal groups of quadratic forms with finite index. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 32 (2023) no. 2, pp. 371-396. doi: 10.5802/afst.1740

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