Mathematics of Computation

Author(s): Arjeh M. Cohen; Scott H. Murray; D. E. Taylor.
Journal: Math. Comp. 73 (2004), 1477-1498.
MSC (2000): Primary 20G15, 20C40
Posted: July 7, 2003
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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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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: 10.1090/S0025-5718-03-01582-5
PII: S 0025-5718(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
Posted: 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.
Copyright of article: Copyright 2003, American Mathematical Society

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