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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
Published electronically: July 7, 2003
MathSciNet review: 2047097
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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

Scott H. Murray
Affiliation: Department of Mathematics and Statistics, University of Sydney, Sydney, New South Wales 2006, Australia

D. E. Taylor
Affiliation: Department of Mathematics and Statistics, University of Sydney, Sydney, New South Wales 2006, Australia

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

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