J. Austral. Math. Soc.  73 (2002), 279-299
Analyse conforme sur les algèbres de Jordan

M. Pevzner
  Université Libre de Bruxelles
  CP 218, Campus de la Plaine
  1050 Brussels

We construct the Weil representation of the Kantor-Koecher-Tits Lie algebra $\mathfrak{g}$ associated to a simple real Jordan algebra $V$. Later we introduce a family of integral operators intertwining the Weil representation with the infinitesimal representations of the degenerate principal series of the conformal group $G$ of the Jordan algebra $V$. The decomposition of $L^2(V)$ in the case of Jordan algebra of real square matrices is given using this construction.
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