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Computing in groups of Lie type |
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| Authors: | Arjeh M Cohen Scott H Murray D E Taylor |
| Institution: | Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands ; Department of Mathematics and Statistics, University of Sydney, Sydney, New South Wales 2006, Australia ; Department of Mathematics and Statistics, University of Sydney, Sydney, New South Wales 2006, Australia |
| 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. |
| Keywords: | Group of Lie type reductive algebraic group computational algebra |
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