Ebook: Algebraic Groups and their Representations

This volume contains 19 articles written by speakers at the Advanced Study Institute on 'Modular representations and subgroup structure of al­ gebraic groups and related finite groups' held at the Isaac Newton Institute, Cambridge from 23rd June to 4th July 1997. We acknowledge with gratitude the financial support given by the NATO Science Committee to enable this ASI to take place. Generous financial support was also provided by the European Union. We are also pleased to acknowledge funds given by EPSRC to the Newton Institute which were used to support the meeting. It is a pleasure to thank the Director of the Isaac Newton Institute, Professor Keith Moffatt, and the staff of the Institute for their dedicated work which did so much to further the success of the meeting. The editors wish to thank Dr. Ross Lawther and Dr. Nick Inglis most warmly for their help in the production of this volume. Dr. Lawther in particular made an invaluable contribution in preparing the volume for submission to the publishers. Finally we wish to thank the distinguished speakers at the ASI who agreed to write articles for this volume based on their lectures at the meet­ ing. We hope that the volume will stimulate further significant advances in the theory of algebraic groups.

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This volume contains articles by 20 leading workers in the field of algebraic groups and related finite groups.

Articles on representation theory are written by Andersen on tilting modules, Carter on canonical bases, Cline, Parshall and Scott on endomorphism algebras, James and Kleshchev on the symmetric group, Littelmann on the path model, Lusztig on homology bases, McNinch on semisimplicity in prime characteristic, Robinson on block theory, Scott on Lusztig's character formula, and Tanisaki on highest weight modules.
Articles on subgroup structure are written by Seitz and Brundan on double cosets, Liebeck on exceptional groups, Saxl on subgroups containing special elements, and Guralnick on applications of subgroup structure.
Steinberg gives a new, short proof of the isomorphism and isogeny theorems for reductive groups.
Aschbacher discusses the classification of quasithin groups and Borovik the classification of groups of finite Morley rank.

Audience: The book contains accounts of many recent advances and will interest research workers and students in the theory of algebraic groups and related areas of mathematics.

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This volume contains articles by 20 leading workers in the field of algebraic groups and related finite groups.

Articles on representation theory are written by Andersen on tilting modules, Carter on canonical bases, Cline, Parshall and Scott on endomorphism algebras, James and Kleshchev on the symmetric group, Littelmann on the path model, Lusztig on homology bases, McNinch on semisimplicity in prime characteristic, Robinson on block theory, Scott on Lusztig's character formula, and Tanisaki on highest weight modules.
Articles on subgroup structure are written by Seitz and Brundan on double cosets, Liebeck on exceptional groups, Saxl on subgroups containing special elements, and Guralnick on applications of subgroup structure.
Steinberg gives a new, short proof of the isomorphism and isogeny theorems for reductive groups.
Aschbacher discusses the classification of quasithin groups and Borovik the classification of groups of finite Morley rank.

Audience: The book contains accounts of many recent advances and will interest research workers and students in the theory of algebraic groups and related areas of mathematics.

Content:
Front Matter....Pages i-xviii
Linear and Nonlinear Group Actions, and the Newton Institute Program....Pages 1-23
Tilting Modules for Algebraic Groups....Pages 25-42
Semisimplicity in Positive Characteristic....Pages 43-52
Homology Bases Arising from Reductive Groups Over a Finite Field....Pages 53-72
Highest Weight Modules Associated to Parabolic Subgroups with Commutative Unipotent Radicals....Pages 73-90
Symmetric Groups and Schur Algebras....Pages 91-102
Branching Rules for Symmetric Groups and Applications....Pages 103-130
Endomorphism Algebras and Representation Theory....Pages 131-149
Representations of Simple Lie Algebras: Modern Variations on a Classical Theme....Pages 151-173
The Path Model, the Quantum Frobenius Map and Standard Monomial Theory....Pages 175-212
Arithmetical Properties of Blocks....Pages 213-232
The Isomorphism and Isogeny Theorems for Reductive Algebraic Groups....Pages 233-240
Double Cosets in Algebraic Groups....Pages 241-257
Dense Orbits and Double Cosets....Pages 259-274
Subgroups of Exceptional Groups....Pages 275-290
Overgroups of Special Elements in Simple Algebraic Groups and Finite Groups of Lie Type....Pages 291-300
Some Applications of Subgroup Structure to Probabilistic Generation and Covers of Curves....Pages 301-320
Quasithin Groups....Pages 321-340
Tame Groups of Odd and Even Type....Pages 341-366
Back Matter....Pages 367-374

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This volume contains articles by 20 leading workers in the field of algebraic groups and related finite groups.

Articles on representation theory are written by Andersen on tilting modules, Carter on canonical bases, Cline, Parshall and Scott on endomorphism algebras, James and Kleshchev on the symmetric group, Littelmann on the path model, Lusztig on homology bases, McNinch on semisimplicity in prime characteristic, Robinson on block theory, Scott on Lusztig's character formula, and Tanisaki on highest weight modules.
Articles on subgroup structure are written by Seitz and Brundan on double cosets, Liebeck on exceptional groups, Saxl on subgroups containing special elements, and Guralnick on applications of subgroup structure.
Steinberg gives a new, short proof of the isomorphism and isogeny theorems for reductive groups.
Aschbacher discusses the classification of quasithin groups and Borovik the classification of groups of finite Morley rank.

Audience: The book contains accounts of many recent advances and will interest research workers and students in the theory of algebraic groups and related areas of mathematics.

Content:
Front Matter....Pages i-xviii
Linear and Nonlinear Group Actions, and the Newton Institute Program....Pages 1-23
Tilting Modules for Algebraic Groups....Pages 25-42
Semisimplicity in Positive Characteristic....Pages 43-52
Homology Bases Arising from Reductive Groups Over a Finite Field....Pages 53-72
Highest Weight Modules Associated to Parabolic Subgroups with Commutative Unipotent Radicals....Pages 73-90
Symmetric Groups and Schur Algebras....Pages 91-102
Branching Rules for Symmetric Groups and Applications....Pages 103-130
Endomorphism Algebras and Representation Theory....Pages 131-149
Representations of Simple Lie Algebras: Modern Variations on a Classical Theme....Pages 151-173
The Path Model, the Quantum Frobenius Map and Standard Monomial Theory....Pages 175-212
Arithmetical Properties of Blocks....Pages 213-232
The Isomorphism and Isogeny Theorems for Reductive Algebraic Groups....Pages 233-240
Double Cosets in Algebraic Groups....Pages 241-257
Dense Orbits and Double Cosets....Pages 259-274
Subgroups of Exceptional Groups....Pages 275-290
Overgroups of Special Elements in Simple Algebraic Groups and Finite Groups of Lie Type....Pages 291-300
Some Applications of Subgroup Structure to Probabilistic Generation and Covers of Curves....Pages 301-320
Quasithin Groups....Pages 321-340
Tame Groups of Odd and Even Type....Pages 341-366
Back Matter....Pages 367-374
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