Geodesic
Enumerating Excedances With Linear Characters In Classical Weyl Groups
Séminaire lotharingien de combinatoire, Tome 74 (2015-2018)

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Several signed excedance-type statistics have nice formulae when summed over the symmetric group and over the hyperoctahedral group. Motivated by these, we consider sums of the form f\chi,n(q) = \sumw in W \chi(w) qexc(w) where W is a classical Weyl group of rank n, \chi is a non-trivial one-dimensional character of W, and exc(w) is the excedance statistic of w.

We give formulae for these sums in a more general multivariate setting. We sharpen existing results for types A and B and give new results for classical Weyl groups of type B and type D. 

@article{SLC_2015-2018_74_a2,
     author = {Sivaramakrishnan Sivasubramanian},
     title = {Enumerating {Excedances} {With} {Linear} {Characters} {In} {Classical} {Weyl} {Groups}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {74},
     year = {2015-2018},
     url = {http://geodesic.mathdoc.fr/item/SLC_2015-2018_74_a2/}
}
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Sivaramakrishnan Sivasubramanian. Enumerating Excedances With Linear Characters In Classical Weyl Groups. Séminaire lotharingien de combinatoire, Tome 74 (2015-2018). http://geodesic.mathdoc.fr/item/SLC_2015-2018_74_a2/