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Séminaire Lotharingien de Combinatoire, B74c (2016), 15 pp.

# Sivaramakrishnan Sivasubramanian

# Enumerating Excedances With Linear Characters In
Classical Weyl Groups

**Abstract.**
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*) =
*\sum*_{w in W} \chi(*w*) *q*^{exc(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.

Received: July 24, 2015.
Revised: April 29, 2016.
Accepted: May 4, 2016.

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