We establish the spectral gap property for dense subgroups of SU (), generated by finitely many elements with algebraic entries; this result was announced in [BG3]. The method of proof differs, in several crucial aspects, from that used in [BG] in the case of SU.
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Jean Bourgain, Alex Gamburd, A spectral gap theorem in SU. J. Eur. Math. Soc. 14 (2012), no. 5, pp. 1455–1511DOI 10.4171/JEMS/337