Sign balance for finite groups of Lie type

Eli Bagno; Yona Cherniavsky

doi:10.1016/j.laa.2008.02.016

Sign balance for finite groups of Lie type

Eli Bagno, Yona Cherniavsky

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

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 F_q calculated in F_q. The Mahonian distribution appears in these formulas.

Original language	English
Pages (from-to)	224-233
Number of pages	10
Journal	Linear Algebra and Its Applications
Volume	429
Issue number	1
DOIs	https://doi.org/10.1016/j.laa.2008.02.016
State	Published - 1 Jul 2008
Externally published	Yes

Keywords

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

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10.1016/j.laa.2008.02.016

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KW - Cyclic sieving phenomenon

KW - Generating functions

KW - Lie groups

KW - Matrix analysis

KW - Sign balance

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JO - Linear Algebra and Its Applications

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Sign balance for finite groups of Lie type

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Keywords

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