Kazhdan-Lusztig cells with unequal parameters

• 作者： Bonnafe, Cedric, author.
• 其他作者：
  • SpringerLink (Online service)
• 其他題名：
  • Algebra and applications ;
• 出版： Cham : Springer International Publishing :Imprint: Springer
• 叢書名： Algebra and applications,volume 24
• 主題： Hecke algebras. , Coxeter groups. , Representations of algebras. , Mathematics. , Group Theory and Generalizations.
• ISBN： 9783319707365 (electronic bk.) 、 9783319707358 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: 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.
• More
• 摘要註: 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.
• 讀者標籤：

  需登入
• 引用連結：

  Copy Link
• 目前引用數
• Share: