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Laguerre semigroup and Dunkl operators
Abstract We construct a two-parameter family of actions ωk,a of the Lie algebra 𝔰𝔩(2,ℝ) by differential–difference operators on ℝN∖{0}. Here k is a multiplicity function for the Dunkl operators,Expand
Knapp–Stein type intertwining operators for symmetric pairs
Abstract For a symmetric pair ( G , H ) of reductive groups we construct a family of intertwining operators between spherical principal series representations of G and H that are induced fromExpand
Analysis on the minimal representation of O(p;q) { I. Realization via conformal geometry
Abstract This is the first in a series of papers devoted to an analogue of the metaplectic representation, namely the minimal unitary representation of an indefinite orthogonal group; thisExpand
Fock model and Segal–Bargmann transform for minimal representations of Hermitian Lie groups
Abstract For any Hermitian Lie group G of tube type we construct a Fock model of its minimal representation. The Fock space is defined on the minimal nilpotent K C -orbit X in p C and the L 2 -innerExpand
Conformally invariant trilinear forms on the sphere
To each complex number $\lambda$ is associated a representation $\pi_\lambda$ of the conformal group $SO_0(1,n)$ on $\mathcal C^\infty(S^{n-1})$ (spherical principal series). For three valuesExpand
Geometry of the Borel -- de Siebenthal Discrete Series
Let G0 be a connected, simply connected real simple Lie group. Suppose that G0 has a compact Cartan subgroup T0, so it has discrete series representations. Relative to T0 there is a distinguishedExpand
Dunkl operators and a family of realizations of osp(1|2)
In this paper, a family of radial deformations of the realization of the Lie superalgebra osp(1|2) in the theory of Dunkl operators is obtained. This leads to a Dirac operator depending on 3Expand
Conformal covariance for the powers of the Dirac operator
A new proof of the conformal covariance of the powers of the flat Dirac operator is obtained. The proof uses their relation with the Knapp-Stein intertwining operators for the spinorial principalExpand
Analysis on the minimal representation of O(p,q) -- III. ultrahyperbolic equations on R^{p-1,q-1}
For the group O(p,q) we give a new construction of its minimal unitary representation via Euclidean Fourier analysis. This is an extension of the q = 2 case, where the representation is the massExpand
Analysis on the minimal representation of O(p,q) II. Branching laws
This is a second paper in a series devoted to the minimal unitary representation of Oðp; qÞ: By explicit methods from conformal geometry of pseudo Riemannian manifolds, we find the branching lawExpand