Sign balance for finite groups of Lie type
Yona Cherniavsky, Eli Bagno
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. The same technique is 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. These formulas are new appearances of the Mahonian distribution.
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