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Twisted Dickson-Mui invariants and the Steinberg module multiplicity

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arxiv 1009.0414 v2 pith:AIDINIK3 submitted 2010-09-02 math.RT math.AT

Twisted Dickson-Mui invariants and the Steinberg module multiplicity

Jinkui Wan , Weiqiang Wang This is my paper
classification math.RT math.AT
keywords algebramodulearbitrarydeterminantexteriorinvariantsmultiplicityproduct
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We determine the invariants, with arbitrary determinant twists, of the parabolic subgroups of the finite general linear group GL_n(q) acting on the tensor product of the symmetric algebra and the exterior algebra of the natural GL_n(q)-module V. In addition, we obtain the graded multiplicity of the Steinberg module of GL_n(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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