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Bilinear and Quadratic Forms on Rational Modules of Split Reductive Groups

Published online by Cambridge University Press:  20 November 2018

Skip Garibaldi  and
Daniel K. Nakano
Skip Garibaldi
Affiliation:
Institute for Pure and Applied Mathematics, UCLA, 460 Portola Plaza, Box 957121, Los Angeles, CA 90095-7121, USA and Center for Communications Research, San Diego, CA 92121, USA e-mail: [email protected]
Daniel K. Nakano
Affiliation:
Department of Mathematics, University of Georgia, Athens, Georgia 30602, USA e-mail: [email protected]
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Abstract

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The representation theory of semisimple algebraic groups over the complex numbers (equivalently, semisimple complex Lie algebras or Lie groups, or real compact Lie groups) and the questions of whether a given complex representation is symplectic or orthogonal have been solved since at least the 1950s. Similar results for Weyl modules of split reductive groups over fields of characteristic different from 2 hold by using similar proofs. This paper considers analogues of these results for simple, induced, and tilting modules of split reductive groups over fields of prime characteristic as well as a complete answer for Weyl modules over fields of characteristic 2.

Keywords

20G0511E3911E8815A6320G15orthogonal representationssymmetric tensorsalternating formscharacteristic 2split reductive groups
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 68 , Issue 2 , 01 April 2016 , pp. 395 - 421
Copyright
Copyright © Canadian Mathematical Society 2016

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