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 $H_ρ$ be an l-parabolic subalgebra of $H$. We give an elementary explicit construction for the basic algebra of a non-simple block of $H_ρ$. We also discuss homological properties of $H_ρ$-modules, in particular existence of varieties for modules, and some consequences.

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