Sign balance for finite groups of Lie type

Eli Bagno, Yona Cherniavsky

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


A product formula for the parity generating function of the number of 1's in invertible matrices over Z2 is given. The computation is based on algebraic tools such as the Bruhat decomposition. It is somewhat surprising that the number of such matrices with odd number of 1's is greater than the number of those with even number of 1's. The same technique can be used to obtain a parity generating function also for symplectic matrices over Z2. We present also a generating function for the sum of entries of matrices over an arbitrary finite field Fq calculated in Fq. The Mahonian distribution appears in these formulas.

Original languageEnglish
Pages (from-to)224-233
Number of pages10
JournalLinear Algebra and Its Applications
Issue number1
StatePublished - 1 Jul 2008
Externally publishedYes


  • Bruhat decomposition
  • Cyclic sieving phenomenon
  • Generating functions
  • Lie groups
  • Matrix analysis
  • Sign balance


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