Geodesic
Enumerating Excedances With Linear Characters In Classical Weyl Groups
Séminaire lotharingien de combinatoire, Tome 74 (2015-2018) 
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/
@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},
     year = {2015-2018},
     volume = {74},
     url = {http://geodesic.mathdoc.fr/item/SLC_2015-2018_74_a2/}
}
TY  - JOUR
AU  - Sivaramakrishnan Sivasubramanian
TI  - Enumerating Excedances With Linear Characters In Classical Weyl Groups
JO  - Séminaire lotharingien de combinatoire
PY  - 2015-2018
VL  - 74
UR  - http://geodesic.mathdoc.fr/item/SLC_2015-2018_74_a2/
ID  - SLC_2015-2018_74_a2
ER  - 
%0 Journal Article
%A Sivaramakrishnan Sivasubramanian
%T Enumerating Excedances With Linear Characters In Classical Weyl Groups
%J Séminaire lotharingien de combinatoire
%D 2015-2018
%V 74
%U http://geodesic.mathdoc.fr/item/SLC_2015-2018_74_a2/
%F SLC_2015-2018_74_a2

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

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.