ON BASES OF SOME SIMPLE MODULES OF SYMMETRIC GROUPS AND HECKE ALGEBRAS

We consider simple modules for a Hecke algebra with a parameter of quantum characteristic e. Equivalently, we consider simple modules D λ, labelled by e-restricted partitions λ of n, for a cyclotomic KLR algebra RΛ0n over a field of characteristic p ≥ 0, with mild restrictions on p. If all parts of λ are at most 2, we identify a set DStde, p (λ) of standard λ-tableaux, which is defined combinatorially and naturally labels a basis of D λ. In particular, we prove that the q-character of D λ can be described in terms of DStde, p (λ). We show that a certain natural approach to constructing a basis of an arbitrary D λ does not work in general, giving a counterexample to a conjecture of Mathas.