  We investigate deformations of skew group algebras arising from the action of
the symmetric group on polynomial rings over fields of arbitrary
characteristic. Over the real or complex numbers, Lusztig's graded affine Hecke
algebra and analogs are all isomorphic to Drinfeld Hecke algebras, which
include the symplectic reflection algebras and rational Cherednik algebras.
Over fields of prime characteristic, new deformations arise that capture both a
disruption of the group action and also a disruption of the commutativity
relations defining the polynomial ring. We classify deformations for the
symmetric group acting in its natural (reducible) reflection representation.
