Polynomial invariants of finite unitary groups
type: Item
instance of: scholarly article
title: Polynomial invariants of finite unitary groups
zbMATH Open document ID: 1112.13010
author: Huah Chu
author: Shin-Yao Jow
published in: Journal of Algebra
publication date: 2006-12-07T00:00:00Z
review text: The present paper deals with the problem of finding the invariants of classical groups over finite fields. The earlier result on this was due to \textit{L. E. Dickson} [American M. S. Trans. 12, 75--98 (1911; JFM 42.0136.01)], which treated the cases of general linear and special linear groups. Another important paper is that of \textit{D. Carlisle} and \textit{P. H. Kropholler} [Bull. Lond. Math. Soc. 24, 57--60 (1992; Zbl 0778.12006)], which explicit generators for the rational invariants of orthogonal and unitary groups, and also found explicit generators and relations for the rings of polynomial invariants of symplectic groups. One should mention that their results showed that these invariant rings are all complete intersections. As for the invariant rings of orthogonal and unitary groups there are several papers dealing with low-dimensional cases and a recent paper [\textit{P. H. Kropholler, S. Mohseni Rajaei} and \textit{J. Segal}, Glasg. Math. J. 47, No. 1, 7--54 (2005; Zbl 1103.13007)] treats the orthogonal groups over \(\mathbb{F}_{2}\), the general case remains open. Let \(U_{n}(\mathbb{F}_{q^{2}})\) be the \(n\)-dimensional unitary group over the finite field \(\mathbb{F}_{q^{2}}\). The goal of this paper is to contribute in solving the above problem, by finding generators and relations for the ring of invariants of \(U_{n}(\mathbb{F}_{q^{2}})\). There is also prove that this is a complete intersection.
Mathematics Subject Classification ID: 13A50
Mathematics Subject Classification ID: 20G40
zbMATH DE Number: 5078143
zbMATH Keywords: modular unitary group
zbMATH Keywords: polynomial invariants
zbMATH Keywords: complete intersection
reviewed by: Marius Tărnăuceanu
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2006.04.002
OpenAlex ID: W1999908278
cites work: Q4273960
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DOI: 10.1016/J.JALGEBRA.2006.04.002
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description: scientific article; zbMATH DE number 5078143