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Signed Mahonian polynomials for classical Weyl groups

Riccardo Biagioli
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Abstract

The generating functions of the major index and of the flag-major index, with each of the one-dimensional characters over the symmetric and hyperoctahedral group, respectively, have simple product formulas. In this paper, we give a factorial-type formula for the generating function of the D-major index with sign over the Weyl groups of type D. This completes a picture which is now known for all the classical Weyl groups.

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Riccardo Biagioli. 2004-04-16. Signed Mahonian polynomials for classical Weyl groups. https://arxiv.org/abs/math/0404300

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