Fundamental domains for congruence subgroups of SL2 in positive characteristic

Lisa Carbone, Leigh Cobbs, Scott H. Murray

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

In this work, we construct fundamental domains for congruence subgroups of SL2(Fq[t]) and PGL2(Fq[t]). Our method uses Gekeler's description of the fundamental domains on the Bruhat-Tits tree X=Xq+1 in terms of cosets of subgroups. We compute the fundamental domains for a number of congruence subgroups explicitly as graphs of groups using the computer algebra system Magma.

Original languageEnglish (US)
Pages (from-to)431-439
Number of pages9
JournalJournal of Algebra
Volume325
Issue number1
DOIs
StatePublished - Jan 1 2011

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Keywords

  • Bruhat-Tits tree
  • Fundamental domain
  • Groups acting on trees
  • Primary
  • Secondary
  • Special linear group

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