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Laguerre semigroup and Dunkl operators

- S. Said, Toshiyuki Kobayashi, B. Orsted
- Mathematics, Physics
- Compositio Mathematica
- 22 July 2009

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

- Jan Mollers, B. Orsted, Y. Oshima
- Mathematics
- 16 September 2013

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 from… Expand

Analysis on the minimal representation of O(p;q) { I. Realization via conformal geometry

- Toshiyuki Kobayashi, B. Orsted
- Mathematics, Physics
- 7 November 2001

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; this… Expand

Fock model and Segal–Bargmann transform for minimal representations of Hermitian Lie groups

- J. Hilgert, Toshiyuki Kobayashi, Jan Mollers, B. Orsted
- Mathematics, Physics
- 25 March 2012

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 -inner… Expand

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 values… Expand

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 distinguished… Expand

Dunkl operators and a family of realizations of osp(1|2)

- H. D. Bie, B. Orsted, P. Somberg, V. Souček
- Mathematics
- 24 November 2009

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 3… Expand

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 principal… Expand

Analysis on the minimal representation of O(p,q) -- III. ultrahyperbolic equations on R^{p-1,q-1}

- Toshiyuki Kobayashi, B. Orsted
- Mathematics, Physics
- 7 November 2001

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 mass… Expand

Analysis on the minimal representation of O(p,q) II. Branching laws

- Toshiyuki Kobayashi, B. Orsted
- Mathematics, Physics
- 7 November 2001

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 law… Expand

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