Reflection factorizations of Singer cycles

J. B. Lewis, V. Reiner, D. Stanton

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


The number of shortest factorizations into reflections for a Singer cycle in GLn(Fq) is shown to be (qn-1)n-1. Formulas counting factorizations of any length, and counting those with reflections of fixed conjugacy classes are also given. The method is a standard character-theory technique, requiring the compilation of irreducible character values for Singer cycles, semisimple reflections, and transvections. The results suggest several open problems and questions, which are discussed at the end.

Original languageEnglish (US)
Pages (from-to)663-691
Number of pages29
JournalJournal of Algebraic Combinatorics
Issue number3
StatePublished - Oct 2 2014

Bibliographical note

Publisher Copyright:
© Springer Science+Business Media New York 2014.


  • Factorization
  • Reflection
  • Singer cycle
  • Transvection


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