Low-dimensional complex characters of the symplectic and orthogonal groups

TL;DR

This paper classifies low-dimensional irreducible complex characters of symplectic and orthogonal groups, providing a detailed understanding of their character degrees up to a specific bound.

Contribution

It offers a comprehensive classification of irreducible complex characters of symplectic and orthogonal groups with degrees below a certain threshold, extending previous character theory results.

Findings

Complete classification of characters up to degree D

Explicit bounds for character degrees in these groups

Identification of all characters within the specified degree range

Abstract

We classify the irreducible complex characters of the symplectic groups $Sp_{2n}(q)$ and the orthogonal groups $Spin_{2n}^\pm(q)$, $Spin_{2n+1}(q)$ 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.