Skip Garibaldi and Anne Quéguiner-Mathieu: Pfister's Theorem for orthogonal involutions of degree $12$

Submission: 2008, Feb 8

We use the fact that a projective half-spin representation of $Spin_{12}$ has an open orbit to generalize Pfister's result on quadratic forms of dimension 12 in the third power of the fundamental ideal to orthogonal involutions.

2000 Mathematics Subject Classification: 20G15; 16W10; 11E04

Keywords and Phrases: Algebraic groups; Orthogonal involutions ; Quadratic forms

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