Low-dimensional representations of special unitary groups

We prove gap results fur the low-dimensional representation of unitary groups in nondefining characteristics. More precisely, we give a lower bound for the third smallest degree of a nontrivial absolutely irreducible representation of the groups mentioned above, which is almost in the order of magnitude of the square of the two smallest such representations. As a corollary we obtain the uniqueness of Well representations in all cross characteristics for the unitary groups. Our approach uses some results on ordinary representations which can be proved using Deligne-Lusztig theory and which might be of independent interest, as well as information on decomposition matrices. (C) 2001 Academic Press.