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Representations of finite groups of Lie type and associated algebras

Objective

The proposed research is in the representation theory of finite groups and algebras and consists of two parts: one focusing on the finite groups of Lie type and their associated algebras, the other part involving the study of Steenrod algebras with the help of A-infinity algebras. In the context of finite groups of Lie type, we propose to show Cabanes-Rickard and apos;s conjecture on Alvis-Curtisduality, beginning with some specific cases. My thesis contains the original construction of a complex H of Hecke algebras of type A, which was shown to induce a derived equivalence; for general linear groups H is linked to the complex inducing the Âlvis-Curtis duality. One research goal is to show that H induces a homotopy equivalence.

But more importantly, one can construct a graded algebra S with the aid of H and relate it via the index representation of the Hecke algebra to the q-Schur algebra. Thus S is a new algebra related to a well-known algebra, making it a most interesting new object. The programme will be hosted b y Dr. Karin Erdmann at the Mathematical Institute, University of Oxford, who is an expert on algebras of this type. Finally, we would study the structure of the group cohomology over the Steenrod algebra and define that structure in a purely algebraic way in terms of the group algebra, with aid of A-infinity algebras. In addition to fostering the development of a young researcher, this programme would reinforce research ties between France and England.

Call for proposal

FP6-2002-MOBILITY-5
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Funding Scheme

EIF - Marie Curie actions-Intra-European Fellowships

Coordinator

THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
Address
University Offices, Wellington Square
Oxford
United Kingdom