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Kazhdan-Lusztig cells with unequal parameters [electronic resource]

Kazhdan-Lusztig cells with unequal parameters [electronic resource]

자료유형
E-Book(소장)
개인저자
Bonnafé, Cédric.
서명 / 저자사항
Kazhdan-Lusztig cells with unequal parameters [electronic resource] / Cédric Bonnafé.
발행사항
Cham :   Springer,   c2017.  
형태사항
1 online resource (xxv, 348 p.) : ill. (some col.).
총서사항
Algebra and applications,1572-5553 ; 24
ISBN
9783319707358 9783319707365 (eBook)
요약
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.
일반주기
Title from e-Book title page.  
내용주기
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.
서지주기
Includes bibliographical references and index.
이용가능한 다른형태자료
Issued also as a book.  
일반주제명
Hecke algebras. Coxeter groups. Representations of algebras.
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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
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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)

소장정보

No. 소장처 청구기호 등록번호 도서상태 반납예정일 예약 서비스
No. 1 소장처 중앙도서관/e-Book 컬렉션/ 청구기호 CR 512.2 등록번호 E14014458 도서상태 대출불가(열람가능) 반납예정일 예약 서비스 M

컨텐츠정보

목차

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.

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