Geodesic
A Semigroup Approach to Linear Algebraic Groups III. Buildings
Canadian journal of mathematics, Tome 38 (1986) no. 3, pp. 751-768

Voir la notice de l'article provenant de la source Cambridge University Press

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 
Putcha, Mohan S. A Semigroup Approach to Linear Algebraic Groups III. Buildings. Canadian journal of mathematics, Tome 38 (1986) no. 3, pp. 751-768. doi: 10.4153/CJM-1986-039-1
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