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Descents and one-dimensional characters for classical Weyl groups

✍ Scribed by Victor Reiner

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
434 KB
Volume
140
Category
Article
ISSN
0012-365X

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✦ Synopsis

This paper examine all sums of the form

where W is a classical Weyl group, g is a one-dimensional character of W, and d(n) is the descent statistic. This completes a picture which is known when Wis the symmetric group S, (the Weyi group A,_ 1). Surprisingly, the answers turn out to be simpler and generalize further for the other classical Weyl groups B,(~ C,) and D.. The B. case uses sign-reversing involutions, while the D. case follows from a result of independent interest relating statistics for all three groups.

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