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Representation Theory
Representation Theory
ISSN 1088-4165

 

Orthogonal representations of twisted forms of $ \operatorname{SL}_2$


Author: Skip Garibaldi
Journal: Represent. Theory 12 (2008), 435-446
MSC (2000): Primary 20G05; Secondary 11E04, 11E76, 20G15
Published electronically: December 8, 2008
MathSciNet review: 2465801
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Abstract: For every absolutely irreducible orthogonal representation of a twisted form of $ \operatorname{SL}_2$ over a field of characteristic zero, we compute the ``unique'' symmetric bilinear form that is invariant under the group action. We also prove the analogous result for Weyl modules in prime characteristic (including characteristic 2) and an isomorphism between two symmetric bilinear forms given by binomial coefficients.


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Additional Information

Skip Garibaldi
Affiliation: Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia 30322
Email: skip@member.ams.org

DOI: http://dx.doi.org/10.1090/S1088-4165-08-00335-X
PII: S 1088-4165(08)00335-X
Received by editor(s): November 6, 2007
Received by editor(s) in revised form: August 4, 2008
Published electronically: December 8, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.