Alexander E. Zalesskii and Pham Huu Tiep

University of East Anglia

University of Florida
 
Title: Minimal Characters of the Finite Classical Groups

Abstract:
  
{Let $G(q)$ be a finite simple group of Lie type over a finite field of
order $q$ and $d(G(q))$ the minimal degree of faithful projective complex
representations of $G(q)$. For the case $G(q)$ is a classical group we determine
the number of projective complex characters of $G(q)$ of degree $d(G(q))$.
In several cases we also determine the projective complex characters of the
second and the third lowest degrees. As a corollary of these results we 
deduce the classification of quasi-simple irreducible complex linear groups
of degree at most $2r$, $r$ a prime divisor of the group order.}

The paper has appeared in Comm. Algebra 24 (1996), 2093 - 2167.