Computing in groups of Lie type

A.M. Cohen; S.H. Murray; D.E. Taylor

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

Computing in groups of Lie type

A.M. Cohen, S.H. Murray, D.E. Taylor

Discrete Algebra and Geometry

Research output: Contribution to journal › Article › Academic › peer-review

33 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1477-1498
Journal	Mathematics of Computation
Volume	73
Issue number	247
DOIs	https://doi.org/10.1090/S0025-5718-03-01582-5
Publication status	Published - 2004

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title = "Computing in groups of Lie type",

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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AB - 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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DO - 10.1090/S0025-5718-03-01582-5

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SP - 1477

EP - 1498

JO - Mathematics of Computation

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Computing in groups of Lie type

Abstract

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