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Open subgroups of locally compact Kac-Moody groups

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Caprace, Pierre-Emmanuel [UCL] Marquis, Timothée [UCL]

Let G be a complete Kac–Moody group over a finite field. It is known that G possesses a BN-pair structure, all of whose parabolic subgroups are open in G . We show that, conversely, every open subgroup of G is contained with finite index in some parabolic subgroup; moreover there are only finitely many such parabolic subgroups. The proof uses some new results on parabolic closures in Coxeter groups. In particular, we give conditions ensuring that the parabolic closure of the product of two elements in a Coxeter group contains the respective parabolic closures of those elements.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès libre
Publication date 2013
Language Anglais
Journal information "Mathematische Zeitschrift" - Vol. 274, no. 1-2, p. 291-313 (2013)
Peer reviewed yes
Publisher Springer ((Germany) Heidelberg)
issn 0025-5874
e-issn 1432-1823
Publication status Publié
Affiliation UCL - SST/IRMP - Institut de recherche en mathématique et physique
Links
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Bibliographic reference Caprace, Pierre-Emmanuel ; Marquis, Timothée. Open subgroups of locally compact Kac-Moody groups. In: Mathematische Zeitschrift, Vol. 274, no. 1-2, p. 291-313 (2013)
Permanent URL http://hdl.handle.net/2078/121004