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

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).