An invariant for triples in the Shilov boudary of a bounded symmetric domain

Jean-Louis Clerc (1)

1 IECN - Institut Élie Cartan de Nancy

Let $\cal D$ be a bounded domain, $G$ its group of biholomorphic diffeomorphisms, and $S$ its Shilov boundary. We define a function $ \iota : S\times S\times S \longrightarrow \Bbb R$ which is invariant under $G$. This invariant generalizes the Maslov index as defined earlier by B. Osrted and the author and the angular invariant constructed by E. Cartan for the unit sphere in $\Bbb C^2$.

Mots clés: bounded symmetric domains; tube type domains; Shilov boundary; automorphy kernel; Euclidean Jordan algebra; Jordan triple system; Maslov index; Cartan's angular invariant

Domaines: Théorie des représentations [math.RT]

Jean-Louis Clerc. An invariant for triples in the Shilov boudary of a bounded symmetric domain. Communications in Analysis and Geometry, 2007, 15, pp.147-174. ⟨hal-00095857⟩