Unfaithful complex hyperbolic triangle groups, III: Arithmeticity and commensurability

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Abstract

We prove that the so-called sporadic complex reflection triangle groups in SU(2, 1) are all nonarithmetic but one, and that they are not commensurable to Mostow or Picard lattices (with a small list of exceptions). This provides an infinite list of potential new nonarithmetic lattices in SU(2, 1).

Original languageEnglish (US)
Pages (from-to)359-372
Number of pages14
JournalPacific Journal of Mathematics
Volume245
Issue number2
DOIs
StatePublished - Apr 1 2010
Externally publishedYes

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Keywords

  • Complex hyperbolic geometry
  • Complex reflection groups
  • Nonarithmetic lattices

ASJC Scopus subject areas

  • Mathematics(all)

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