Consider a complex projective space with its Fubini-Study metric. We study certain one parameter deformations of this metric on the complement of an arrangement (= finite union of hyperplanes) whose Levi-Civita connection is of Dunkl type. Interesting examples are obtained from the arrangements defined by finite complex reflection groups. We determine a parameter interval for which the metric is locally of Fubini-Study type, flat, or complex-hyperbolic. We find a finite subset of this interval for...

Let $G$ be a quasi-Hermitian Lie group with Lie algebra $𝔤$ and $K$ be a compactly embedded subgroup of $G$. Let ${\xi }_0$ be a regular element of ${𝔤}^{*}$ which is fixed by $K$. We give an explicit $G$-equivariant diffeomorphism from a complex domain onto the coadjoint orbit $𝒪\left({\xi }_0\right)$ of ${\xi }_0$. This generalizes a result of [B. Cahen, Berezin quantization and holomorphic representations, Rend. Sem. Mat. Univ. Padova, to appear] concerning the case where $𝒪\left({\xi }_0\right)$ is associated with a unitary irreducible representation of $G$ which is holomorphically...

Nous présentons quelques résultats au sujet des groupes engendrés par trois involutions antiholomorphes dans le cadre du plan hyperbolique complexe ${\mathbf{H}}_{ℂ}^2$.