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 noninv O (w) on w in W that counts the number of ""O -noninversions"" of w . This generalises the classical (non-)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 noninv 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.
Introduction Defining the operators The case where O contains only hyperplanes Equivariant theory of BHR random walks The family ? (2 k ,1 n?2k) The original family ? (k,1 n?k) Acknowledgements Appendix A. G n -module decomposition of ? (k,1 n?k) Bibliography List of Symbols Index