Sign balance for finite groups of Lie type
Cherniavsky, Yona · Bagno, Eli
Original · EN
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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