By Leonard Scott (auth.), R. W. Carter, J. Saxl (eds.)
This quantity comprises 19 articles written via audio system on the complicated examine Institute on 'Modular representations and subgroup constitution of al gebraic teams and similar finite teams' held on the Isaac Newton Institute, Cambridge from twenty third June to 4th July 1997. We recognize with gratitude the monetary help given via the NATO technology Committee to allow this ASI to occur. beneficiant monetary aid used to be additionally supplied by way of the eu Union. we're additionally happy to recognize cash given by means of EPSRC to the Newton Institute that have been used to aid the assembly. it's a excitement to thank the Director of the Isaac Newton Institute, Professor Keith Moffatt, and the employees of the Institute for his or her devoted paintings which did loads to extra the good fortune of the assembly. The editors desire to thank Dr. Ross Lawther and Dr. Nick Inglis so much warmly for his or her assist in the construction of this quantity. Dr. Lawther particularly made a useful contribution in getting ready the quantity for submission to the publishers. eventually we want to thank the celebrated audio system on the ASI who agreed to put in writing articles for this quantity in response to their lectures on the meet ing. we are hoping that the quantity will stimulate additional major advances within the idea of algebraic groups.
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Additional resources for Algebraic Groups and their Representations
W. (1995) Subgroups of simple algebraic groups and of related finite and locally finite groups of Lie type, in B. Hartley et al. ), Finite and Locally Finite Groups (Istanbul, 1994), NATO ASI series, vol. 471, Kluwer Academic Publishers, Dordrecht, pp. 71-96. 68. W. (1998) Subgroups of exceptional groups, pp. 275-290 of this volume. 69. E. and Saxl, J. (1987) A classification of the maximal subgroups of the finite alternating and symmetric groups, J. Algebra 111, 365-383. 70. E. and Saxl, J. (1988) On the O'Nan-Scott theorem for finite primitive permutation groups, J.
A remarkable converse has recently been proved by Erdmann . To explain the connection between the nondefining and defining characteristic problems, we first consider the better-known case where the prime p divides q - 1. As Dipper and James have observed, character formulas for GL(r,q) unipotent bloeks in these cases would give character formulas for all q-Schur algebras in characteristic p with the parameter q specialized to I-that is, for all Schur algebras in characteristic p. It is well-known  that this gives all irreducible representations for the algebraic groups GL(n, k) over algebraically closed fields k of characteristic p.
Parshall, B. and Scott, L. (1998) Stratifying endomorphism algebras associated to Hecke algebras, J. Algebra 203, 169-210. , Parshall, B. and Scott, L. (1998) Cells and q-Schur algebras, J. Transformation Groups 3, 33-49. , Parshall, B. and Scott, L. (1998) Quantum Weyl reciprocity and tilting modules, Comm. Math. Physics, to appear. Du, J. and Scott, L. (1994) Lusztig conjectures, old and new, I, J. Reine Angew. Math. 455, 141-182. Du, J. and Scott, L. (1998) The q-Schur 2 algebra, Trans. Amer.