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Abstract for 
Victor Reiner,  The distribution of descents and length in a Coxeter group

We give a method for computing the $q$-{\it Eulerian distribution} 
$$
W(t,q)=\sum_{w \in W} t^{{\rm des}(w)} q^{l(w)}
$$
as a rational function in $t$ and $q$,
where $(W,S)$ is an arbitrary Coxeter system, $l(w)$ is the {\it length
function} in $W$, and ${\rm des}(w)$ is the number of simple reflections
$s \in S$ for which $l(ws)<l(w)$.  Using this we compute generating 
functions encompassing the $q$-Eulerian distributions of the classical
infinite families of finite and affine Weyl groups.

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