Invariant cones in Lie algebras, Lie semigroups, and the holomorphic discrete series

Spherical functions on ordered symmetric spaces

“…The associated semigroup S is given by S = exp(C)7:f and S is homeomorphic to C x H (cf. [0181], Theorem 3.5). Moreover M with this causal structure is globally hyperbolic (cf.…”

Function spaces on the Olśhanskiĭsemigroup and the Gel'fand-Gindikin program

“…It is easy to check that r° is both left and right invariant under U(l, 1) (this in general follows from OPshanskil [17]), and also from (8) that I ± 7 in non-singular for all 7 € F 0 . But then the last assertion follows immediately.…”

“…The semigroup property gives the following characterization of r° due to OPshanskil [17]. where one of the conditions to be in r° reads…”

Noyau de Cauchy-Szegö d'un espace symétrique de type Cayley

“…5), Oishanskii associe un semi-groupe r(C) contenu dans le groupe complexifié G^ de la forme r(C)=Gexp(iC) (cf. [Ols81], Theorem 3.5). Soit Cmax (resp.…”