On Modular Vector Invariant Fields
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Published:2020-11-05
Issue:04
Volume:27
Page:749-752
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ISSN:1005-3867
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Container-title:Algebra Colloquium
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language:en
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Short-container-title:Algebra Colloq.
Affiliation:
1. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
Abstract
Let [Formula: see text] be a finite field of any characteristic and [Formula: see text] be the general linear group over [Formula: see text]. Suppose W denotes the standard representation of [Formula: see text], and [Formula: see text] acts diagonally on the direct sum of W and its dual space W∗. Let G be any subgroup of [Formula: see text]. Suppose the invariant field [Formula: see text], where [Formula: see text] in [Formula: see text] are homogeneous invariant polynomials. We prove that there exist homogeneous polynomials [Formula: see text] in the invariant ring [Formula: see text] such that the invariant field [Formula: see text] is generated by [Formula: see text] over [Formula: see text].
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Algebra and Number Theory