The Flag Major Index and Group Actions on Polynomial Rings

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Abstract

A new extension of the major index, defined in terms of Coxeter elements, is introduced. For the classical Weyl groups of type B, it is equidistributed with length. For more general wreath products it appears in an explicit formula for the Hilbert series of the (diagonal action) invariant algebra.

Original languageEnglish
Pages (from-to)431-446
Number of pages16
JournalEuropean Journal of Combinatorics
Volume22
Issue number4
DOIs
StatePublished - May 2001

Bibliographical note

Funding Information:
Thanks to Richard Stanley, Dominique Foata, Christian Krattenthaler, Igor Pak and Victor Reiner for their comments. Both authors were supported in part by the Israel Science Foundation and by internal research grants from Bar-Ilan University.

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