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

^*此作品的通讯作者

数学学院

University of Virginia

科研成果: 期刊稿件 › 文章 › 同行评审

2 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	43-57
页数	15
期刊	Mathematical Proceedings of the Cambridge Philosophical Society
卷	151
期	1
DOI	https://doi.org/10.1017/S0305004111000120
出版状态	已出版 - 7月 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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N2 - 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.

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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