The nonexistence of certain Tits geometries with affine diagram
This paper supplies part of the proof of the main theorem in the author's paper in Geom. Dedicata 25, 71-120 (1988; Zbl 0639.51009). In particular, it deals with geometries that are one node extensions of spherical buildings leading to an affine diagram of rank at least four, and so it encompasses the interesting examples arising in the conclusion of the theorem (characteristic 2 and type \(\tilde D_ 4\), \(\tilde A_ 3\), \(\tilde B_ 3).\) The proofs depend on the classification of failure of factorization modules for residue stabilizers which are obtained from the action on the geometry related to the chamber system.
scientific article; zbMATH DE number 4094267