Determinantally Homogeneous Polynomials on Representations of Euclidean Jordan Algebras

Jean-Louis Clerc

Abstract: The classical notion of determinantally homogeneous polynomial is presented in the context of representations of Euclidean Jordan algebras. When the Jordan algebra is of classical type, the study of the algebra of determinantally homogeneous polynomials is strongly related to classical invariant theory and a fairly complete description is obtained. For the Euclidean Jordan algebra of Lorentzian type, the representations are related to Clifford modules. In this case, only partial results are obtained, including complete answers for pinor spaces associated to Clifford algebras of low dimension.

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