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Sign balance for finite groups of Lie type

Yona Cherniavsky·Eli Bagno
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Abstract

A product formula for the parity generating function of the number of 1's in invertible matrices over Z_2 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 Z_2. We present also a generating function for the sum of entries of matrices over an arbitrary finite field F_q calculated in F_q. These formulas are new appearances of the Mahonian distribution.

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Yona Cherniavsky, Eli Bagno. 2005-02-22. Sign balance for finite groups of Lie type. https://arxiv.org/abs/math/0502463

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