Lay Summary. The set of symmetries of a geometric object (for example, the rotations and reflections which leave it looking the same) form what is called a group. The abstraction of this gives rise to the notion of an abstract group, and representation theory is concerned with the reverse process: trying to find suitable geometric objects of which an abstract group can be regarded as symmetries.

This project will look at the representation theory of so-called classical groups of matrices whose entries come from a set of "numbers" called a p-adic field. Parts of the representation theory of these groups are governed by the algebra of certain functions on them. We will compute this algebra, to understand, in particular, a connection which should exist between the algebras for symplectic and orthogonal groups.

Publications

Final report