Computing in groups of Lie type
Authors:
Arjeh M. Cohen, Scott H. Murray and D. E. Taylor
Journal:
Math. Comp. 73 (2004), 1477-1498
MSC (2000):
Primary 20G15, 20C40
DOI:
https://doi.org/10.1090/S0025-5718-03-01582-5
Published electronically:
July 7, 2003
MathSciNet review:
2047097
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We describe two methods for computing with the elements of untwisted groups of Lie type: using the Steinberg presentation and using highest weight representations. We give algorithms for element arithmetic within the Steinberg presentation. Conversion between this presentation and linear representations is achieved using a new generalisation of row and column reduction.
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Additional Information
Arjeh M. Cohen
Affiliation:
Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
Email:
A.M.Cohen@tue.nl
Scott H. Murray
Affiliation:
Department of Mathematics and Statistics, University of Sydney, Sydney, New South Wales 2006, Australia
Email:
murray@maths.usyd.edu.au
D. E. Taylor
Affiliation:
Department of Mathematics and Statistics, University of Sydney, Sydney, New South Wales 2006, Australia
Email:
D.Taylor@maths.usyd.edu.au
DOI:
https://doi.org/10.1090/S0025-5718-03-01582-5
Keywords:
Group of Lie type,
reductive algebraic group,
computational algebra
Received by editor(s):
January 24, 2002
Received by editor(s) in revised form:
December 15, 2002
Published electronically:
July 7, 2003
Additional Notes:
This paper was written during a stay of the first two authors at the University of Sydney. They wish to thank the institute for its hospitality.
Article copyright:
© Copyright 2003
American Mathematical Society