On the Decomposition Numbers of the Ree Groups 2F4(q^2) in Non-Defining Characteristic

TL;DR

This paper computes the modular decomposition matrices of Ree groups 2F4(q^2) for primes greater than 3, determining minimal degrees of non-trivial irreducible representations and providing new insights into their modular representation theory.

Contribution

It provides the first comprehensive computation of the l-modular decomposition matrices for Ree groups 2F4(q^2) for all primes l > 3, including partial results for l=3.

Findings

Decomposition matrices for primes l > 3 are explicitly computed.

Smallest degrees of non-trivial irreducible representations are determined.

Results include partial 3-modular decomposition matrices.

Abstract

We compute the l-modular decomposition matrices of the simple Ree groups 2F4(q^2), where q^2=2^{2n+1} and n is a positive integer, for all primes l > 3 up to some entries in the unipotent characters. Using these matrices we determine the smallest degree of a non-trivial irreducible l-modular representation of 2F4(q^2) for all primes l > 3. We also obtain results on the 3-modular decomposition matrices of 2F4(q^2).