The tensor product of exceptional representations on the general linear group

The exceptional representations are certain infinite-dimensional projective representations of the general linear group over a local field, somewhat analogous to the Weil representations of the symplectic group. We examine the decomposition of the tensor product of two exceptional representations. Our main results concern the multiplicity with which a given representation may occur in this product and the restrictions imposed upon a representation of the principal series by the assumption that it does occur. (C) 2001 Editions scientifiques et medicales Elsevier SAS.