Spectra of symmetrized shuffling operators

Spectra of symmetrized shuffling operators / Reiner, Victor.

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Bibliographic Details
Main Author: Reiner, Victor
Other Authors: Saliola, Franco, Welker, Volkmar
Format: eBook
Language:English
Published: [Place of publication not identified] : [publisher not identified], 2014.
Series:Memoirs of the American Mathematical Society.
Subjects:
Combinatorial group theory.
Markov processes.
Finite groups.
Combinatorial group theory
Finite groups
Markov processes
Online Access:Click for online access
Table of Contents:
  • ""Contents""; ""Chapter I. Introduction""; ""1. The original family of matrices""; ""2. Using the -action""; ""3. An eigenvalue integrality principle""; ""4. A broader context, with more surprises""; ""5. Outline of the paper""; ""Chapter II. Defining the operators""; ""1. Hyperplane arrangements and definition of _{ }""; ""2. Semidefiniteness""; ""3. Equivariant setting""; ""4. â??â??-action and inversions versus noninversions""; ""5. Real reflection groups""; ""6. The case where is a single -orbit""; ""7. A reduction to isotypic components""
  • ""8. Perron-Frobenius and primitivity""""Chapter III. The case where \OOO contains only hyperplanes""; ""1. Review of twisted Gelfand pairs""; ""2. A new twisted Gelfand pair""; ""3. Two proofs of Theorem\nonbreakingspace I.4.1""; ""4. The eigenvalues and eigenspace representations""; ""5. Relation to linear ordering polytopes""; ""Chapter IV. Equivariant theory of \BHR random walks""; ""1. The face semigroup""; ""2. The case relevant for _{ }""; ""3. Some non-equivariant theory""; ""4. Equivariant structure of eigenspaces""; ""5. (Ã?â??â??)-equivariant eigenvalue filtration""
  • ""6. Consequences for the kernels""""7. Reformulation of _{ _{ }}""; ""Chapter V. The family _{(2^{ },1^{ -2 })}""; ""1. A Gelfand model for _{ }""; ""2. Proof of Theorem\nonbreakingspace I.4.3""; ""Chapter VI. The original family _{(,1^{
  • })}""; ""1. Proof of Theorem\nonbreakingspace I.1.1""; ""2. The kernel filtration and block-diagonalization""; ""3. The (unsigned) maps on injective words""; ""4. The complex of injective words""; ""5. Pieri formulae for _{ } and _{ }Ã?â??â??""; ""6. Some derangement numerology""
  • ""7. (_{ }Ã?â??â??)-structure of the first kernel""""8. (_{ }Ã?â??â??)-structure of the kernel filtration""; ""9. Desarrangements and the random-to-top eigenvalue of a tableaux""; ""10. Shaving tableaux""; ""11. Fixing a small value of and letting grow.""; ""12. The representation ^{( -1,1)}""; ""Chapter VII. Acknowledgements""; ""Appendix A. \symm_{ }-module decomposition of _{(,1^{
  • })}""; ""Bibliography""; ""\nomname""; ""Index""

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