Writing projective representations over subfields

Authors

Stephen P. Glasby, Central Washington University
C. R. Leedham-Green, Queen Mary University of London
E. A. O'Brien, University of Auckland

Document Type

Article

Department or Administrative Unit

Mathematics

Publication Date

1-1-2006

Abstract

Let G=〈X〉be an absolutely irreducible subgroup of GL(d, K), and let F be a proper subfield of the finite field K. We present a practical algorithm to decide constructively whether or not G is conjugate to a subgroup of GL(d, F).K×, where K× denotes the centre of GL(d, K). If the derived group of G also acts absolutely irreducibly, then the algorithm is Las Vegas and costs O(|X|d³+d²log|F|) arithmetic operations in K. This work forms part of a recognition project based on Aschbacher’s classification of maximal subgroups of GL(d, K).

Comments

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This article was originally published in Journal of Algebra. The full-text article from the publisher can be found here.

Recommended Citation

Glasby, Stephen P.; Leedham-Green, C. R.; and O'Brien, E. A., "Writing projective representations over subfields" (2006). All Faculty Scholarship for the College of the Sciences. 238.
https://digitalcommons.cwu.edu/cotsfac/238

Journal

Journal of Algebra

Rights

© 2005 Elsevier Inc. All rights reserved.