Geodesic
A Characterization of the Unitary Highest Weight Modules by Euclidean Jordan Algebras
Zhanqiang Bai1
1Dept. of Mathematics, Hong Kong University, of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
Journal of Lie Theory, Tome 23 (2013) no. 3, pp. 747-778

Voir la notice de l'article provenant de la source Heldermann Verlag

\def\c{{\frak c}} \def\o{{\frak o}} \def\C{{\Bbb C}} Let $\c\o(J)$ be the conformal algebra of a simple Euclidean Jordan algebra $J$. We show that a (non-trivial) unitary highest weight $\c\o(J)$-module has the smallest positive Gelfand-Kirillov dimension if and only if a certain quadratic relation is satisfied in the universal enveloping algebra $U(\c\o(J)_\C)$. In particular, we find an quadratic element in $U(\c\o(J)_\C)$. A prime ideal in $U(\c\o(J)_\C)$ equals the Joseph ideal if and only if it contains this quadratic element.
Classification : 22E47, 17B10, 17C99
Mots-clés : Euclidean Jordan algebras, unitary highest weight module, quadratic relation, Joseph Ideal

Zhanqiang Bai  1

1 Dept. of Mathematics, Hong Kong University, of Science and Technology, Clear Water Bay, Kowloon, Hong Kong 
Zhanqiang Bai. A Characterization of the Unitary Highest Weight Modules by Euclidean Jordan Algebras. Journal of Lie Theory, Tome 23 (2013) no. 3, pp. 747-778. http://geodesic.mathdoc.fr/item/JOLT_2013_23_3_a8/
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     author = {Zhanqiang Bai},
     title = {A {Characterization} of the {Unitary} {Highest} {Weight} {Modules} by {Euclidean} {Jordan} {Algebras}},
     journal = {Journal of Lie Theory},
     pages = {747--778},
     year = {2013},
     volume = {23},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2013_23_3_a8/}
}
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