Spectra of Symmetrized Shuffling Operators

ISBN-13: 9780821890950 / Angielski

Victor Reiner;Franco Saliola;Volkmar Welker

Opis

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.

Spis treści

• 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