Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-05T03:26:32.137Z Has data issue: false hasContentIssue false

Principal indecomposable modules for some three-dimensional special linear groups

Published online by Cambridge University Press:  17 April 2009

James Archer
Affiliation:
Department of Pure Mathematics, University of Sydney, Sydney, New South Wales 2006, Australia.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let k be a finite field of characteristic 2, and let G be the three dimensional special linear group over k. The principal indecomposable modules of G over k are constructed from tensor products of the irreducible modules, and formulae for their dimensions are given.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1980

References

[1]Alperin, J.L., “Protective modules and tensor products”, J. Pure Appl. Algebra 8 (1976), 235241.CrossRefGoogle Scholar
[2]Alperin, J.L., “Projective modules for SL(2, 2 n) ”, preprint.Google Scholar
[3]Curtis, Charles W., Reiner, Irving, Representation theory of finite groups and associative algebras (Pure and Applied Mathematics, 11. Interscience [John Wiley & Sons], New York, London, Sydney, 1962. Reprinted, 1966).Google Scholar
[4]Steinberg, Robert, “Representations of algebraic groups”, Nagoya Math. J. 22 (1963), 3356.CrossRefGoogle Scholar
[5]Steinberg, Robert, “Prime power representations of finite linear groups”, Canad. J. Math. 8 (1956), 580591.CrossRefGoogle Scholar