Twisted Dickson-Mui invariants and the Steinberg module multiplicity
Abstract
We determine the invariants, with arbitrary determinant twists, of the parabolic subgroups of the finite general linear group GLn(q) acting on the tensor product of the symmetric algebra and the exterior algebra of the natural GLn(q)-module V. In addition, we obtain the graded multiplicity of the Steinberg module of GLn(q) in the tensor product of the symmetric algebra and the exterior algebra of V, twisted by an arbitrary determinant power.
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