On the decomposition numbers of the Ree groups [formula omitted] in non-defining characteristic

Abstract

We compute the ℓ-modular decomposition matrices of the simple Ree groups F 4 2 ( q 2 ) , where q 2 = 2 2 n + 1 and n > 0 , for all primes ℓ > 3 up to some entries in the unipotent and one entry in the non-unipotent characters. We determine the smallest degree of a nontrivial irreducible ℓ-modular representation of F 4 2 ( q 2 ) for all primes ℓ > 3 and also obtain results on the 3-modular decomposition matrices of F 4 2 ( q 2 ) .