03940nam a22004695i 4500 978-3-319-70736-5 DE-He213 20210619041059.0 cr nn 008mamaa 180507s2017 gw | s |||| 0|eng d 9783319707365 978-3-319-70736-5 10.1007/978-3-319-70736-5 doi QA174-183 PBG bicssc MAT002010 bisacsh PBG thema 512.2 23 Bonnafé, Cédric. author. aut http://id.loc.gov/vocabulary/relators/aut Kazhdan-Lusztig Cells with Unequal Parameters [electronic resource] / by Cédric Bonnafé. 1st ed. 2017. Cham : Springer International Publishing : Imprint: Springer, 2017. XXV, 348 p. 28 illus., 15 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Algebra and Applications, 1572-5553 ; 24 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. 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. Group theory. Group Theory and Generalizations. https://scigraph.springernature.com/ontologies/product-market-codes/M11078 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783319707358 Printed edition: 9783319707372 Printed edition: 9783030099862 Algebra and Applications, 1572-5553 ; 24 https://doi.org/10.1007/978-3-319-70736-5 ZDB-2-SMA ZDB-2-SXMS Mathematics and Statistics (SpringerNature-11649) Mathematics and Statistics (R0) (SpringerNature-43713)