For a finite real reflection group W and a W -orbit O of flats in its reflection arrangement - or equivalently a conjugacy class of its parabolic subgroups - the authors introduce a statistic ninv O (w) on w in W that counts the number of O -ninversions of w . This generalises the classical (n-)inversion statistic for permutations w in the symmetric group S n. The authors then study the operator ? O of right-multiplication within the group algebra CW by the element that has ninv O (w) as its coefficient on w.
Victor Reiner , University of Minnesota, Minneapolis, Minnesota. Franco Saliola , Universite du Quebec a Montreal, Canada. Volkmar Welker , Philipps-Universitaet Marburg, Germany.