Robert M. Guralnick and Pham Huu Tiep

University of Southern California

University of Florida
 
Title: Low-dimensional Representations of Special Linear Groups in
Cross Characteristics

Abstract:
  {The low-dimensional projective irreducible representations in cross
characteristics of the projective special linear group $PSL_{n}(q)$ are 
investigated. If $n \geq 3$ and $(n,q) \neq (3,2)$, $(3,4)$, $(4,2)$, $(4,3)$,
all such representations of the first degree (which is 
$(q^{n}-q)/(q-1) - \kappa$ with $\kappa = 0$ or $1$) and the second degree 
(which is $(q^{n}-1)/(q-1)$) come from Weil representations. We show that the 
gap between the second and the third degree is roughly $q^{2n-4}$.}

The paper has appeared in Proc. London Math. Soc. 78 (1999), 116 - 138.