Computing in groups of Lie type

Cohen, Arjeh; Murray, Scott; Taylor, D.

doi:10.1090/S0025-5718-03-01582-5

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
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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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