Low-dimensional complex characters of the symplectic and orthogonal groups

Abstract

We classify the irreducible complex characters of the symplectic groups $S{p}_{2n}(q)$ and the orthogonal groups $Spi{n}_{2n}^{\pm }(q)$, $Spi{n}_{2n+1}(q)$ of degrees up to the bound D, where $D=(q^n-1)q^{4n-10}/2$ for symplectic groups, $D=q^{4n-8}$ for orthogonal groups in odd dimension, and $D=q^{4n-10}$ for orthogonal groups in even dimension.

44 pages. Comm. Algebra, to appear