Descents and one-dimensional characters for classical Weyl groups Original Research Article

This paper examine all sums of the form σπϵWχ(π)td(π) where W is a classical Weyl group, X is a one-dimensional character of W, and d(π) is the descent statistic. This completes a picture which is known when W is the symmetric group Sn (the Weyl group An−1). Surprisingly, the answers turn out to be simpler and generalize further for the other classical Weyl groups Bn(≊Cn) and Dn. The Bn, case uses sign-reversing involutions, while the Dn case follows from a result of independent interest relating statistics for all three groups.