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Some Groups of Type E7

Published online by Cambridge University Press:  11 January 2016

T. A. Springer
T. A. Springer*
Affiliation:
Mathematisch Instituut, Budapestlaan 6, 3584 CD Utrecht, the Netherlands, springer@math.uu.nl
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Abstract

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An algebraic group of type E7 over an algebraically closed field has an irreducible representation in a vector space of dimension 56 and is, in fact, the identity component of the automorphism group of a quartic form on the space. This paper describes the construction of the quartic form if the characteristic is ≠ 2, 3, taking into account a field of definition F. Certain F-forms of E7 appear in the automorphism groups of quartic forms over F, as well as forms of E6. Many of the results of the paper are known, but are perhaps not easily accessible in the literature.

Keywords

20G1520G10
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 182: Special Issue Celebrating the 60th Birthday of George Lusztig , June 2006 , pp. 259 - 284
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2006

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