Kazhdan-Lusztig Cells with Unequal Parameters / by Cédric Bonnafé.

Format:

Book

Author/Creator:

Bonnafé, Cédric., Author.

Series:

Algebra and Applications, 1572-5553 ; 24

Language:

English

Subjects (All):

Group theory.

Group Theory and Generalizations.

Local Subjects:

Group Theory and Generalizations.

Physical Description:

1 online resource (XXV, 348 p. 28 illus., 15 illus. in color.)

Edition:

1st ed. 2017.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2017.

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 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.

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.

Notes:

Includes bibliographical references and index.

ISBN:

3-319-70736-1