# Low-dimensional representations of finite orthogonal groups

## TL;DR

This paper investigates the minimal irreducible Brauer characters of finite orthogonal groups, establishing their smallest degrees and a gap result indicating a quadratic increase for larger characters under certain conditions.

## Contribution

It identifies the smallest irreducible Brauer characters for finite orthogonal groups and proves a degree gap result in non-defining characteristic.

## Key findings

- Smallest irreducible Brauer characters are determined.
- A quadratic gap between the smallest and next larger characters is established.
- Results depend on certain restrictions on the characteristic.

## Abstract

We determine the smallest irreducible Brauer characters for finite quasi-simple orthogonal type groups in non-defining characteristic. Under some restrictions on the characteristic we also prove a gap result showing that the next larger irreducible Brauer characters have a degree roughly the square of those of the smallest non-trivial characters.