p-adic automorphic functions for the unitairy group in three variables, by King Fai Lai and Harm Voskuil

An updated version of this paper appears as preprint 0202 and so this preprint has been removed. Let K be a p-adic field and let L be a quadratic extension of K. We assume that the characteristic of the residue field of K is not two. We consider the action of the unitairy group SU(3,L) on the projective plane. For a discrete cocompact subgroup of SU(3,L) we construct p-adic automorphic functions. There are two different constructions. One uses infinite products. The other uses infinite sums of torus invariants. These functions are well-defined on an open analytic subspace Y of the projective plane. This space Y consists of the points in the projective plane that are stable for all maximal K-split tori of the group SU(3,L). An important ingredient of the proofs is the relation of the space Y with the Bruhat-Tits building of the group SU(3,L).

King Fai Lai and Harm Voskuil <kflai@maths.usyd.edu.au ; voskuil@math.rug.nl>