Inclusions of irreducible spherical buildings of equal rank \(\geq3\) (Q2471467)

Each rank 2 residue of an irreducible spherical building of rank at least 3 is a Moufang polygon and such polygons have been classified by \textit{J. Tits} and \textit{R. M. Weiss} [Moufang Polygons. Springer Monographs in Mathematics. Berlin: Springer (2002; Zbl 1010.20017)]. In the paper under review the author adopts a local approach to buildings via their rank 2 residues to investigate inclusions of irreducible spherical buildings of equal rank at least 3. Two such buildings have the same Tits diagram and isomorphic Weyl groups and one is a subbuilding of the other. Based on his determination [Forum Math. 17, 921--957 (2005; Zbl 1093.51007)] of all algebraic inclusions of Moufang quadrangles such that none of the root groups is 2-torsion, which corresponds to the fact that the characteristic of the underlying skew field is different from 2, the author obtains a classification of inclusions of irreducible spherical buildings of higher rank. The case where the Tits diagram has only simple edges is straightforward and corresponds to a (skew) field and a subfield over which the respective buildings are defined. The remaining cases, where there is exactly one residue which is a Moufang quadrangle, are more involved and are covered in a case by case study under the additional assumption that the characteristics of the defining fields are different from 2 in these cases.