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

Author(s): Skip Garibaldi
Journal: Represent. Theory 12 (2008), 435-446.
MSC (2000): Primary 20G05; Secondary 11E04, 11E76, 20G15
Posted: December 8, 2008
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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: 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
Posted: December 8, 2008
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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