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Spectra of Symmetrized Shuffling Operators

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Spectra of Symmetrized Shuffling Operators Synopsis

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.

About This Edition

ISBN: 9780821890950
Publication date:
Author: Victor Reiner, Franco Saliola, Volkmar Welker
Publisher: American Mathematical Society
Format: Paperback
Pagination: 109 pages
Series: Memoirs of the American Mathematical Society
Genres: Algebraic geometry
Probability and statistics
Algebra