Descents and one-dimensional characters for classical Weyl groups

Victor Reiner

Research output: Contribution to journalArticle

24 Scopus citations

Abstract

This paper examine all sums of the form σ πε{lunate}Wχ(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.

Original languageEnglish (US)
Pages (from-to)129-140
Number of pages12
JournalDiscrete Mathematics
Volume140
Issue number1-3
DOIs
StatePublished - Jun 11 1995

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