Titlebook: Buildings of Spherical Type and Finite BN-Pairs; Jacques Tits Book 1974 Springer-Verlag Berlin Heidelberg 1974 Finite.Morphism.algebra.alg

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Distributionen und Greensche Funktion,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

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Distributionen und Greensche Funktion,ings of rank 2. Here, similar results are obtained for BN-pairs (13.5, 13.32); it will be seen that the proofs are considerably simpler than that of 4.1.2. In 13.5, an arbitrary group G with BN-pair (B,N) appears as an amalgamated sum of the parabolic subgroups “of rank 2” containing B, but we shall

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Buildings of Spherical Type and Finite BN-Pairs978-3-540-38349-9Series ISSN 0075-8434 Series E-ISSN 1617-9692

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Buildings,onditions hold:. It is clear that Δ is a chamber complex and that the apartments are isomorphic subcomplexes. We shall see (3.15) that the isomorphism class of the apartments is entirely determined by Δ. More precisely, it can be shown that if a complex Δ possesses a set α of subcomplexes such that