Abstract
Let G be the simple, simply connected algebraic group SL 3 defined over an algebraically closed field K of characteristic p > 0. In this article, we find H 2(G, V) for any irreducible G-module V. When p > 7, we also find H 2(G(q), V) for any irreducible G(q)-module V for the finite Chevalley groups G(q) = SL(3, q) where q is a power of p.
2000 Mathematics Subject Classification:
ACKNOWLEDGMENTS
Some of the work in this article was prepared towards the author's PhD qualification under the supervision of Prof. M. W. Liebeck, with financial support from the EPSRC. We would like to thank Prof. Liebeck for his help in producing this article. Also we thank the anonymous referee for many helpful suggestions and corrections, and the editor P. Tiep for his suggestion to extend the work to cover the finite groups of Lie type.
Notes
Recent work by the author together with B. Parshall and L. Scott answers Question 3.10 in the affirmative, with no condition on p but depending on the root system. That result is then used to give answers to Question 3.8 also.
Communicated by P. Tiep.