On l-parabolic Hecke algebras of symmetric groups

Let $H=H_q(n)$ be the Hecke algebra of the symmetric group of degree n, over a field of arbitrary characteristic, and where q is a primitive l-th root of unity in $K$. Let $H_{\rho}$ be an l-parabolic subalgebra of $H$. We give an elementary explicit construction for the basic algebra of a non-simple block of $H_{\rho}$. We also discuss homological properties of $H_{\rho}$-modules, in particular existence of varieties for modules, and some consequences.