A characterization of the unitary highest weight modules by Euclidean Jordan algebras

Details A characterization of the unitary highest weight modules by Euclidean Jordan algebras A characterization of the unitary highest weight modules by Euclidean Jordan algebras

2012-03-29

arxiv.org/abs/1203.6434v3

Mathematics

Representation Theory

25pages

Scientific paper

Let ($G$, $K$) be a tube type Hermitian symmetric pair. Then the Lie algebra $\mathfrak{g}_{0}$ of $G$ equals the conformal algebra $\mathfrak{co}(J)$ of a simple Euclidean Jordan algebra $J$. Actually this correspondence is one-to-one. A (non-trivial) unitary highest weight module of the conformal algebra $\mathfrak{co}(J)$ has the minimal Gelfand-Kirillov dimension if and only if a certain quadratic relation is satisfied in the universal enveloping algebra of $\mathfrak{co}(J)$.

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