Twisted Dickson-Mui invariants and the Steinberg module multiplicity

Jinkui Wan; Weiqiang Wang

doi:10.1017/S0305004111000120

Twisted Dickson-Mui invariants and the Steinberg module multiplicity

Jinkui Wan^*, Weiqiang Wang

^*Corresponding author for this work

School of Mathematics and Statistics

University of Virginia School of Engineering and Applied Science

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

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 S^̇(V) and the exterior algebra ∧^̇(V) of the natural GL_n(q)- module V. In addition, we obtain the graded multiplicity of the Steinberg module of GL_n(q) in S^̇(V) ⊗ ∧^̇(V), twisted by an arbitrary determinant power.

Original language	English
Pages (from-to)	43-57
Number of pages	15
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	151
Issue number	1
DOIs	https://doi.org/10.1017/S0305004111000120
Publication status	Published - Jul 2011

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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 {\.S}(V) and the exterior algebra {\.∧}(V) of the natural GLn(q)- module V. In addition, we obtain the graded multiplicity of the Steinberg module of GLn(q) in {\.S}(V) ⊗ {\.∧}(V), twisted by an arbitrary determinant power.",

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AB - 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 Ṡ(V) and the exterior algebra ∧̇(V) of the natural GLn(q)- module V. In addition, we obtain the graded multiplicity of the Steinberg module of GLn(q) in Ṡ(V) ⊗ ∧̇(V), twisted by an arbitrary determinant power.

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Twisted Dickson-Mui invariants and the Steinberg module multiplicity

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