On the decomposition numbers of the Ree groups in non-defining characteristic

We compute the ℓ-modular decomposition matrices of the simple Ree groups , where q2=22n+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 for all primes ℓ>3 and also obtain results on the 3-modular decomposition matrices of .