Computing in groups of Lie type
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- by Arjeh M. Cohen, Scott H. Murray and D. E. Taylor PDF
- Math. Comp. 73 (2004), 1477-1498 Request permission
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.References
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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
- 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.
- © Copyright 2003 American Mathematical Society
- Journal: Math. Comp. 73 (2004), 1477-1498
- MSC (2000): Primary 20G15, 20C40
- DOI: https://doi.org/10.1090/S0025-5718-03-01582-5
- MathSciNet review: 2047097