On the dimension of some modular irreducible representations of affine Hecke algebras of type A

Let $K$ be a field and $q$ be an invertible element in $K$. Let $\H_{n}^{\aff}$ be the type $A$ affine Hecke algebra (or degenerate affine Hecke algebra) over $K$. Let $l$ be the smallest positive integer such that $1+q+\cdots+q^{l-1}=0$ in $K$. In this talk, I will describe how to construct, for each $(l,m)$-special skew shape diagram, a completely splittable modular irreducible $\H_{n}^{\aff}$-modules, which generalize earlier work of O. Mathieu, H. Wenzl and A. Ram.