JournalsjemsVol. 14, No. 5pp. 1455–1511

A spectral gap theorem in SU(d)(d)

  • Jean Bourgain

    Institute for Advanced Study, Princeton, United States
  • Alex Gamburd

    University of California at Santa Cruz, United States
A spectral gap theorem in SU$(d)$ cover
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Abstract

We establish the spectral gap property for dense subgroups of SU(d)(d) (d2d\geq 2), 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(2)(2).

Cite this article

Jean Bourgain, Alex Gamburd, A spectral gap theorem in SU(d)(d). J. Eur. Math. Soc. 14 (2012), no. 5, pp. 1455–1511

DOI 10.4171/JEMS/337