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A Semigroup Approach to Linear Algebraic Groups III. Buildings

Published online by Cambridge University Press:  20 November 2018

Mohan S. Putcha
Mohan S. Putcha*
Affiliation:
North Carolina State University, Raleigh, North Carolina
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Introduction. Let K be an algebraically closed field, G = SL(3, K) the group of 3 × 3 matrices over K of determinant 1. Let denote the monoid of all 3 × 3 matrices over K. If e is an idempotent in , then

are opposite parabolic subgroups of G in the usual sense [1], [28]. However the map

does not exhaust all pairs of opposite parabolic subgroups of G. Now consider the representation ϕ:G → SL(6, K) given by

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 38 , Issue 3 , 01 June 1986 , pp. 751 - 768
Copyright
Copyright © Canadian Mathematical Society 1986

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