Affine polar spaces derived from symplectic spaces, their geometry and representations: alternating semiforms

Abstract

Deleting a hyperplane from a polar space associated with a symplectic polarity we get a specific, symplectic, affine polar space. Similar geometry, called an \afsempol\ arises as a result of generalization of the notion of an alternating form to a semiform. Some properties of these two geometries are given and their automorphism groups are characterized.