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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.
List of contents
Linear and nonlinear group actions, and the Newton Institute program.- Tilting modules for algebraic groups.- Semisimplicity in positive characteristic.- Homology bases arising from reductive groups over a finite field.- Highest weight modules associated to parabolic subgroups with commutative unipotent radicals.- Symmetric groups and Schur algebras.- Branching rules for symmetric groups and applications.- Endomorphism algebras and representation theory.- Representations of simple Lie algebras: modern variations on a classical theme.- The path model, the quantum Frobenius map and standard monomial theory.- Arithmetical properties of blocks.- The isomorphism and isogeny theorems for reductive algebraic groups.- Double cosets in algebraic groups.- Dense orbits and double cosets.- Subgroups of exceptional groups.- Overgroups of special elements in simple algebraic groups and finite groups of Lie type.- Some applications of subgroup structure to probabilistic generation and covers of curves.- Quasithin groups.- Tame groups of odd and even type.
Summary
Proceedings of the NATO Advanced Study Institute on Modular Representations and Subgroup Structure of Algebraic Groups and Related Finite Groups, Cambridge, U.K., 23 June-4 July 1997
