![Kazhdan-Lusztig cells with unequal parameters [electronic resource]](https://image.aladin.co.kr/product/11990/20/cover/3319707353_2.jpg)
| 000 | 00000cam u2200205 a 4500 | |
| 001 | 000045988706 | |
| 005 | 20190704160252 | |
| 006 | m d | |
| 007 | cr | |
| 008 | 190703s2017 sz a ob 001 0 eng d | |
| 020 | ▼a 9783319707358 | |
| 020 | ▼a 9783319707365 (eBook) | |
| 040 | ▼a 211009 ▼c 211009 ▼d 211009 | |
| 050 | 4 | ▼a QA174-183 |
| 082 | 0 4 | ▼a 512/.2 ▼2 23 |
| 084 | ▼a 512.2 ▼2 DDCK | |
| 090 | ▼a 512.2 | |
| 100 | 1 | ▼a Bonnafé, Cédric. |
| 245 | 1 0 | ▼a Kazhdan-Lusztig cells with unequal parameters ▼h [electronic resource] / ▼c Cédric Bonnafé. |
| 260 | ▼a Cham : ▼b Springer, ▼c c2017. | |
| 300 | ▼a 1 online resource (xxv, 348 p.) : ▼b ill. (some col.). | |
| 490 | 1 | ▼a Algebra and applications, ▼x 1572-5553 ; ▼v 24 |
| 500 | ▼a Title from e-Book title page. | |
| 504 | ▼a Includes bibliographical references and index. | |
| 505 | 0 | ▼a 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. |
| 520 | ▼a 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. | |
| 530 | ▼a Issued also as a book. | |
| 538 | ▼a Mode of access: World Wide Web. | |
| 650 | 0 | ▼a Hecke algebras. |
| 650 | 0 | ▼a Coxeter groups. |
| 650 | 0 | ▼a Representations of algebras. |
| 830 | 0 | ▼a Algebra and applications ; ▼v 24. |
| 856 | 4 0 | ▼u https://oca.korea.ac.kr/link.n2s?url=https://doi.org/10.1007/978-3-319-70736-5 |
| 945 | ▼a KLPA | |
| 991 | ▼a E-Book(소장) |
Holdings Information
| No. | Location | Call Number | Accession No. | Availability | Due Date | Make a Reservation | Service |
|---|---|---|---|---|---|---|---|
| No. 1 | Location Main Library/e-Book Collection/ | Call Number CR 512.2 | Accession No. E14014458 | Availability Loan can not(reference room) | Due Date | Make a Reservation | Service |
Contents information
Table of Contents
Intro -- Preface -- Acknowledgements -- Contents -- General Notation -- List of Figures -- Summary -- Part I Preliminaries -- 1 Preorders on Bases of Algebras -- 1.1. Definitions -- 1.1.A. Preorders -- 1.1.B. Cells -- 1.1.C. Cell Modules -- 1.1.D. Examples -- 1.2. Preorders and Symmetrizing Forms -- 2 Lusztig''s Lemma -- 2.1. Invariant Bases -- 2.2. Base Change -- Part II Coxeter Systems, Hecke Algebras -- 3 Coxeter Systems -- 3.1. Characterizations of Coxeter Systems -- 3.2. First Properties -- 3.3. Reflections, Roots -- 3.4. Braided Maps -- 3.5. Bruhat Order -- 3.6. Parabolic Subgroups -- 3.7. Longest Element, Left and Right Descent Set -- 3.8. More on Reflections -- 3.9. Conjugacy Classes of Involutions -- 3.10. Fixed Points under Automorphisms -- 3.11. Geometric Representation -- 3.11.A. Coxeter Matrix, Coxeter Graph -- 3.11.B. Reflection Representation -- 3.11.C. Irreducibility -- 3.12. Some Classification Results -- 3.12.A. Finiteness -- 3.12.B. Tame Groups -- 3.12.C. Hyperbolic Coxeter Systems -- 3.13. Tits Cone, Coxeter Complex -- 3.14. Drawing Coxeter Groups -- 3.14.A. Rank 2 -- 3.14.B. Rank 3 -- 4 Hecke Algebras -- 4.1. Definition, First Properties -- 4.1.A. Basis -- 4.1.B. Parabolic Subalgebras -- 4.1.C. Anti-involution -- 4.1.D. Central Form -- 4.2. The Case where A is a Group Algebra -- 4.2.A. Index, Sign -- 4.2.B. Central Form -- 4.2.C. Invertibility -- 4.2.D. Involutions -- 4.3. Functoriality, Parameters -- 4.3.A. Changing the Group -- 4.3.B. Generic Hecke Algebra -- 4.3.C. Changing Signs -- 4.3.D. Vanishing Parameters -- 4.4. r-Polynomials -- 4.5. Reflection Representation -- Part III Kazhdan–Lusztig Cells -- 5 The Kazhdan–Lusztig Basis -- 5.1. Degree, Valuation, Properties of A -- 5.2. The Kazhdan–Lusztig Basis -- 5.3. Kazhdan–Lusztig Polynomials -- 5.4. Functoriality, Parameters -- 5.4.A. Changing mathcalA -- 5.4.B. Changing Signs -- 5.4.C. Vanishing Parameters -- 5.5. Structure Constants -- 5.6. An Algorithm -- 5.7. Examples -- 6 Kazhdan–Lusztig Cells -- 6.1. Preorders on W -- 6.1.A. Cells -- 6.1.B. Cell Modules -- 6.2. Functoriality, Parameters -- 6.2.A. Changing the Group -- 6.2.B. Changing Signs -- 6.2.C. Vanishing Parameters -- 6.3. Descent Sets -- 6.4. About the Structure Constants λx,ys and ρx,ys -- 6.5. Some Conjectures -- 6.6. Drawing Kazhdan–Lusztig Cells -- 6.7. Examples -- 7 Semicontinuity -- 7.1. Faces, Chambers -- 7.2. Cells -- 7.3. Examples -- Part IV General Properties of Cells -- 8 Cells and Parabolic Subgroups -- 8.1. The Kazhdan–Lusztig–Geck Basis -- 8.2. Induction Theorems -- 8.3. The Restriction Theorem -- 8.4. Induction of Isomorphic Cells -- 8.4.A. Definition, Examples -- 8.4.B. Induction -- 8.4.C. About Strongness -- 9 Descent Sets, Knuth Relations and Vogan Classes -- 9.1. Enhanced Descent Sets -- 9.2. Knuth Relations -- 9.3. Vogan Classes -- 10 The Longest Element and Duality in Finite Coxeter Groups -- 10.1. About ω0 -- 10.2. The Inversion Formula -- 10.3. Cells, Structure Constants -- 10.4. Cell Module.
