Abstract
We say that a building (resp. a BN-pair) is of irreducible type if its diagram (resp. the diagram of the corresponding building: cf. 3.2.6) is irreducible. The main result of this section is that all BN-pairs characterized in the title are “provided by” algebraic simple groups over finite fields in the known standard way (for a precise statement, cf. theorem 11.7). This is an easy consequence of the analogous statement for buildings (theorem 11.4), which itself follows readily from the results of the previous sections.
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© 1974 Springer-Verlag Berlin Heidelberg
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(1974). Finite BN-pairs of irreducible type and rank ≥ 3. In: Buildings of Spherical Type and Finite BN-Pairs. Lecture Notes in Mathematics, vol 386. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-38349-9_11
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DOI: https://doi.org/10.1007/978-3-540-38349-9_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-06757-3
Online ISBN: 978-3-540-38349-9
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