Spectra of Symmetrized Shuffling Operators

Victor Reiner, Franco Saliola, Volkmar Welker (Autoren)

Buch | Softcover

109 Seiten

2014
American Mathematical Society (Verlag)
978-0-8218-9095-0 (ISBN)

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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

Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Gewicht	456 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	0-8218-9095-6 / 0821890956
ISBN-13	978-0-8218-9095-0 / 9780821890950
Zustand	Neuware