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INVARIANT RINGS OF ORTHOGONAL GROUPS OVER ${\mathbb F}_2$

Published online by Cambridge University Press:  31 January 2005

P. H. KROPHOLLER ,
S. MOHSENI RAJAEI  and
J. SEGAL
P. H. KROPHOLLER
Affiliation:
Dept. of Mathematics, University of Glasgow, University Gardens, Glasgow G12 8QW e-mail: p.h.kropholler@maths.gla.ac.uk
S. MOHSENI RAJAEI
Affiliation:
Departement of Mathematics, Azzahra University, Vanak, Tehran, Iran e-mail: rajaei@azzahra.ac.ir
J. SEGAL
Affiliation:
Stegemühlenweg 70, 37083 Göttingen e-mail: joel@berlin.com
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Abstract

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We determine the rings of invariants $S^G$ where $S$ is the symmetric algebra on the dual of a vector space $V$ over ${\mathbb F}_2$ and $G$ is the orthogonal group preserving a non-singular quadratic form on $V$. The invariant ring is shown to have a presentation in which the difference between the number of generators and the number of relations is equal to the minimum possibility, namely $\dim V$, and it is shown to be a complete intersection. In particular, the rings of invariants computed here are all Gorenstein and hence Cohen-Macaulay.

Keywords

13A5020G40
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 47 , Issue 1 , January 2005 , pp. 7 - 54
Copyright
2005 Glasgow Mathematical Journal Trust