Orthogonal representations of twisted forms of 𝑆𝐿₂

Garibaldi, Skip

doi:10.1090/S1088-4165-08-00335-X

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

Represent. Theory 12 (2008), 435-446

DOI: https://doi.org/10.1090/S1088-4165-08-00335-X

Published electronically: 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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