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Representations of hecke algebras at roots of unity

Author: Meinolf Geck; Nicolas Jacon
Publisher: London ; New York : Springer, ©2011.
Series: Algebras and applications, v. 15.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
The modular representation theory of Iwahori-Hecke algebras and this theory's connection to groups of Lie type is an area of rapidly expanding interest; it is one that has also seen a number of breakthroughs in recent years. In classifying the irreducible representations of Iwahori-Hecke algebras at roots of unity, this book is a particularly valuable addition to current research in this field. Using the framework  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Geck, Meinolf.
Representations of Hecke Algebras at roots of unity.
London : Springer, ©2011
(DLC) 2011929782
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Meinolf Geck; Nicolas Jacon
ISBN: 9780857297167 0857297163
OCLC Number: 733543760
Description: 1 online resource (xii, 401 pages).
Contents: Preface; Contents; 1 Generic Iwahori-Hecke Algebras; 1.1 Coxeter Groups and Weight Functions; 1.2 Representations of H; 1.3 Lusztig's a-Invariants; 1.4 Balanced Representations; 1.5 The Asymptotic Algebra; 1.6 Introducing Cells; 1.7 Examples of Cells; 1.8 Cells and Leading Coefficients; 2 Kazhdan-Lusztig Cells and Cellular Bases; 2.1 The Kazhdan-Lusztig Basis; 2.2 A Pre-order Relation on Irr(W); 2.3 On Lusztig's Conjectures, I; 2.4 On Lusztig's Conjectures, II; 2.5 On Lusztig's Conjectures, III; 2.6 A Cellular Basis for H; 2.7 Further Properties of the Cellular Basis of H. 2.8 The Case of the Symmetric Group3 Specialisations and Decomposition Maps; 3.1 Grothendieck Groups and Decomposition Maps; 3.2 Canonical Basic Sets; 3.3 Principal Specialisations and Blocks of Defect 1; 3.4 Towards Canonical Basic Sets for Classical Types; 3.5 A Canonical Basic Set for the Symmetric Group; 3.6 Factorisation of Decomposition Maps; 3.7 The General Version of James's Conjecture; 3.8 Blocks and Bad Specialisations; 4 Hecke Algebras and Finite Groups of Lie Type; 4.1 The Schur Functor and its Variations; 4.2 Hom Functors and Harish-Chandra Series. 4.3 Unipotent Principal Series Representations, I4.4 Unipotent Principal Series Representations, II; 4.5 Examples and Conjectures; 4.6 A First Approach to Type Bn; 5 Representation Theory of Ariki-Koike Algebras; 5.1 The Complex Reflection Group of Type G(l,1,n); 5.2 Basic Properties of Ariki-Koike Algebras; 5.3 Ariki-Koike Algebras as Cellular Algebras; 5.4 Decomposition Maps for Ariki-Koike Algebras; 5.5 Cyclotomic Ariki-Koike Algebras; 5.6 A Fock Datum for Ariki-Koike Algebras; 5.7 FLOTW Multipartitions; 5.8 On Basic Sets for Ariki-Koike Algebras. 6 Canonical Bases in Affine Type A and Ariki's Theorem6.1 The Quantum Affine Algebra Uq(sle); 6.2 The Fock Space and Ariki's Theorem; 6.3 Crystal and Canonical Bases for Highest Weight Modules; 6.4 Computing Decomposition Matrices of Ariki-Koike Algebras; 6.5 Uglov's Theory of Fock Spaces; 6.6 Canonical Bases for Fock Spaces; 6.7 Computation of Canonical Basic Sets for Iwahori-Hecke Algebras; 6.8 Recent Developments and Conjectures; 7 Decomposition Numbers for Exceptional Types; 7.1 Algorithmic Methods; 7.2 Decomposition Matrices for W of Dihedral Type. 7.3 Decomposition Matrices for W of Type F47.4 Decomposition Matrices for Types H3, H4, E6, E7, E8; References; Index.
Series Title: Algebras and applications, v. 15.
Responsibility: Meinolf Geck, Nicolas Jacon.
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Abstract:

Fulfilling a valuable need in the field, this volume classifies the irreducible representations of Iwahori-Hecke algebras at roots of unity. The text develops an analogue of James' (1970)  Read more...

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From the reviews:"This book unifies and summaries some of the work, mostly done during the last ten years, on representations of Iwahori-Hecke algebras of finite Coxeter groups. ... The book is very Read more...

 
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