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 a nalogous to the Weil representations of the symplectic group. We examine th e decomposition of the tensor product of two exceptional representations. O ur main results concern the multiplicity with which a given representation may occur in this product and the restrictions imposed upon a representatio n of the principal series by the assumption that it does occur. (C) 2001 Ed itions scientifiques et medicales Elsevier SAS.