Overview
- Provides a self-contained introduction to Kazhdan-Lusztig cells
- Includes figures of the partition into cells for small finite, affine, or hyperbolic Coxeter groups
- Explains Geck and Guilhot induction results, as well as the action of the cactus group
- Reviews and adds substantial results to an active field of research
Part of the book series: Algebra and Applications (AA, volume 24)
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Table of contents (26 chapters)
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Front Matter
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Preliminaries
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Front Matter
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Coxeter Systems, Hecke Algebras
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Front Matter
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Kazhdan–Lusztig Cells
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Front Matter
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Lusztig’s a-Function
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Front Matter
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Keywords
About this book
This monograph provides a comprehensive introduction to the Kazhdan-Lusztig theory of cells in the broader context of the unequal parameter case.
Serving as a useful reference, the present volume offers a synthesis of significant advances made since Lusztig’s seminal work on the subject was published in 2002. The focus lies on the combinatorics of the partition into cells for general Coxeter groups, with special attention given to induction methods, cellular maps and the role of Lusztig's conjectures. Using only algebraic and combinatorial methods, the author carefully develops proofs, discusses open conjectures, and presents recent research, including a chapter on the action of the cactus group.
Kazhdan-Lusztig Cells with Unequal Parameters will appeal to graduate students and researchers interested in related subject areas, such as Lie theory, representation theory, and combinatorics of Coxeter groups. Useful examples and various exercises make this book suitable for self-study and use alongside lecture courses.
Information for readers: The character {\mathbb{Z}} has been corrupted in the print edition of this book and appears incorrectly with a diagonal line running through the symbol.
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Kazhdan-Lusztig Cells with Unequal Parameters
Authors: Cédric Bonnafé
Series Title: Algebra and Applications
DOI: https://doi.org/10.1007/978-3-319-70736-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG, part of Springer Nature 2017
Hardcover ISBN: 978-3-319-70735-8Published: 24 May 2018
Softcover ISBN: 978-3-030-09986-2Published: 14 December 2018
eBook ISBN: 978-3-319-70736-5Published: 07 May 2018
Series ISSN: 1572-5553
Series E-ISSN: 2192-2950
Edition Number: 1
Number of Pages: XXV, 348
Number of Illustrations: 13 b/w illustrations, 15 illustrations in colour
Topics: Group Theory and Generalizations