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Kazhdan-Lusztig cells with unequal parameters

Author: Cédric Bonnafé
Publisher: Cham, Switzerland : Springer, [2017]
Series: Algebras and applications, v. 24.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Bonnafé, Cédric.
Kazhdan-Lusztig cells with unequal parameters.
Cham, Switzerland : Springer, [2017]
(OCoLC)1006461110
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Cédric Bonnafé
ISBN: 9783319707365 3319707361
OCLC Number: 1035556376
Description: 1 online resource
Contents: Part I Preliminaries --
1 Preorders on Bases of Algebras --
2 Lusztig?s Lemma --
Part II Coxeter Systems, Hecke Algebras --
3 Coxeter Systems --
4 Hecke Algebras --
Part III Kazhdan?Lusztig Cells --
5 The Kazhdan?Lusztig Basis --
6 Kazhdan?Lusztig Cells --
7 Semicontinuity --
Part IV General Properties of Cells --
8 Cells and Parabolic Subgroups --
9 Descent Sets, Knuth Relations and Vogan Classes --
10 The Longest Element and Duality in Finite Coxeter Groups --
11 The Guilhot Induction Process --
12 Submaximal Cells (Split Case) --
13 Submaximal Cells (General Case) --
Part V Lusztig?s a-Function --
14 Lusztig?s Conjectures --
15 Split and quasi-split cases --
Part VI Applications of Lusztig?s Conjectures --
16 Miscellanea --
17 Multiplication by Tw0 --
18 Action of the Cactus Group --
19 Asymptotic Algebra --
20 Automorphisms --
Part VII Examples --
21 Finite Dihedral Groups --
22 The Symmetric Group --
23 Affine Weyl Groups of Type A2 --
24 Free Coxeter Groups --
25 Rank 3 --
26 Some Bibliographical Comments --
Appendices --
A Symmetric Algebras --
B Reflection Subgroups of Coxeter Groups --
References --
Index.
Series Title: Algebras and applications, v. 24.
Responsibility: Cédric Bonnafé.

Abstract:

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  Read more...

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