1Institut Elie Cartan, Université Henri Poincaré, 54506 Vandoevre-lès-Nancy, France 2The 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. 3[
Journal of Lie Theory, Tome 12 (2002) no. 1, pp. 113-136
Citer cet article
Jean-Louis Clerc. Determinantally Homogeneous Polynomials on Representations of Euclidean Jordan Algebras. Journal of Lie Theory, Tome 12 (2002) no. 1, pp. 113-136. http://geodesic.mathdoc.fr/item/JOLT_2002_12_1_a6/
@article{JOLT_2002_12_1_a6,
author = {Jean-Louis Clerc},
title = {Determinantally {Homogeneous} {Polynomials} on {Representations} of {Euclidean} {Jordan} {Algebras}},
journal = {Journal of Lie Theory},
pages = {113--136},
year = {2002},
volume = {12},
number = {1},
url = {http://geodesic.mathdoc.fr/item/JOLT_2002_12_1_a6/}
}
TY - JOUR
AU - Jean-Louis Clerc
TI - Determinantally Homogeneous Polynomials on Representations of Euclidean Jordan Algebras
JO - Journal of Lie Theory
PY - 2002
SP - 113
EP - 136
VL - 12
IS - 1
UR - http://geodesic.mathdoc.fr/item/JOLT_2002_12_1_a6/
ID - JOLT_2002_12_1_a6
ER -
%0 Journal Article
%A Jean-Louis Clerc
%T Determinantally Homogeneous Polynomials on Representations of Euclidean Jordan Algebras
%J Journal of Lie Theory
%D 2002
%P 113-136
%V 12
%N 1
%U http://geodesic.mathdoc.fr/item/JOLT_2002_12_1_a6/
%F JOLT_2002_12_1_a6
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.
