Spectral gaps in $ \mathit{SU}(d)$

Jean Bourgain; Alexander Gamburd

doi:10.1016/j.crma.2010.04.024

Group Theory

Spectral gaps in

SU (d)

Presented by: Jean Bourgain

Jean Bourgain ¹; Alexander Gamburd ²

¹ IAS, 1 Einstein Drive, Princeton, NJ 08540, USA
² UCSC, 1156 High Street, Santa Cruz, CA 95064, USA

Comptes Rendus. Mathématique, Volume 348 (2010) no. 11-12, pp. 609-611.

Abstract (Original language)
Résumé

It is shown that if $g_{1}, \dots, g_{k}$ are algebraic elements in $SU (d)$ generating a dense subgroup, then the corresponding Hecke operator has a spectral gap.

On démontre que si $g_{1}, \dots, g_{k}$ sont des éléments algébriques de $SU (d)$ et le groupe engendré par $g_{1}, \dots, g_{k}$ est dense, alors l'opérateur de Hecke défini par ces éléments a un trou spectral.

Received: 2010-04-09
Accepted: 2010-04-15
Published online: 2010-05-04

DOI: 10.1016/j.crma.2010.04.024

Author's affiliations:

Jean Bourgain ¹; Alexander Gamburd ²

¹ IAS, 1 Einstein Drive, Princeton, NJ 08540, USA
² UCSC, 1156 High Street, Santa Cruz, CA 95064, USA

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     author = {Jean Bourgain and Alexander Gamburd},
     title = {Spectral gaps in $ \mathit{SU}(d)$},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {609--611},
     publisher = {Elsevier},
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     number = {11-12},
     year = {2010},
     doi = {10.1016/j.crma.2010.04.024},
     language = {en},
}

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Jean Bourgain; Alexander Gamburd. Spectral gaps in $ \mathit{SU}(d)$. Comptes Rendus. Mathématique, Volume 348 (2010) no. 11-12, pp. 609-611. doi : 10.1016/j.crma.2010.04.024. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.04.024/

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