A characterization of geometries of type E_{7, 4} and E_{8, 4}
by
Silvia Onofrei
Kansas State University

Let \Delta = (P, L) be a parapolar space which is locally A_{n, 3}, n=6, 7. There are two classes of maximal singular subspaces [`A] (which are PG(4)'s) and [`B] (which are PG(n-1)'s). It is proved that there exists a class of 2-convex subspaces D, each subspace isomorphic to D_{5, 5}. Every symplecton of \Delta is contained in a unique element of D. Let \Gamma be a locally D-truncated geometry over K = {P, L, [`A], [`B], D }, where D is a diagram over I of exceptional type E_m, m=7, 8. A residually connected sheaf defined over all nonempty flags of \Gamma is constructed. Then \Delta is the homomorphic image of a building geometry [`(\Delta)] over I, belonging to the diagram D, and the truncation of \Delta to K is isomorphic to \Gamma.

Date received: March 1, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagg-13.