Les noyaux de Bergman et Szegö pour des domaines strictment pseudo-convexes qui généralisent la boule.

Título original Les noyaux de Bergman et Szegö pour des domaines strictment pseudo-convexes qui généralisent la boule.
Título inglés Bergman and Szegö kernels for strictly pseudoconvex domains which generalize the ball.
Título español Núcleos de Bergman y Szegö para dominios estrictamente pseudoconvexos que generalizan la bola.
Autor/es Loeb, Jean-Jacques
Organización Dép. Math. Fac. Sci. Univ. Angers, Angers, Francia
Revista 0214-1493
Publicación 1992, 36 (1): 65-72, 7 Ref.
Tipo de documento articulo
Idioma Francés
Resumen inglés Let G be a complex semi-simple group with a compact maximal group K and an irreducible holomorphic representation ρ on a finite dimensional space V. There exists on V a K-invariant Hermitian scalar product. Let Ω be the intersection of the unit ball of V with the G-orbit of a dominant vector. Ω is a generalization of the unit ball (case obtained for G = SL(n,C) and ρ the natural representation on Cn).
We prove that for such manifolds, the Bergman and Szegö kernels as for the ball are rational fractions of the scalar products and these fractions can be computed explicitely, using invariants of ρ. To compute this kernels, one uses a good orthonormal basis related to ρ, and then proves that one has a rational fraction, using Schur's orthogonality relations and Weyl's dimensional formula for V.
Clasificación UNESCO 120213 ; 120106
Palabras clave español Dominios pseudoconvexos ; Bases ortonormales ; Bola unidad ; Núcleo
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