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Minimal characters of the finite classical groups. (English) Zbl 0901.20031
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 the authors determine the number of projective complex characters of \(G(q)\) of degree \(d(G(q))\). In several cases they also determine the projective complex characters of the second and the third lowest degrees. As a corollary of these results they deduce the classification of quasi-simple irreducible complex linear groups of degree at most \(2r\), \(r\) a prime divisor of the group order.

MSC:
20G05 Representation theory for linear algebraic groups
20C33 Representations of finite groups of Lie type
20C25 Projective representations and multipliers
20G20 Linear algebraic groups over the reals, the complexes, the quaternions
20D05 Finite simple groups and their classification
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