Determinantally Homogeneous Polynomials on Representations of Euclidean Jordan Algebras
Journal of Lie Theory, Volume 12 (2002) no. 1, pp. 113-136
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.
@article{JOLT_2002_12_1_a6,
author = {J.-L. 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},
doi = {10.5802/jolt.255},
zbl = {1061.17026},
url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.255/}
}
TY - JOUR AU - J.-L. 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 - https://jolt.centre-mersenne.org/articles/10.5802/jolt.255/ DO - 10.5802/jolt.255 ID - JOLT_2002_12_1_a6 ER -
J.-L. Clerc. Determinantally Homogeneous Polynomials on Representations of Euclidean Jordan Algebras. Journal of Lie Theory, Volume 12 (2002) no. 1, pp. 113-136. doi: 10.5802/jolt.255
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