English

Finite reflection groups and the Dunkl-Laplace differential-difference operators in conformal geometry

Differential Geometry 2013-05-06 v1 Representation Theory

Abstract

For a finite reflection subgroup GO(n+1,1,\mR)G\leq O(n+1,1,\mR) of the conformal group of the sphere with standard conformal structure (Sn,[g0])(S^n,[g_0]), we geometrically derive differential-difference Dunkl version of the series of conformally invariant differential operators with symbols given by powers of Laplace operator. The construction can be regarded as a deformation of the Fefferman-Graham ambient metric construction of GJMS operators.

Keywords

Cite

@article{arxiv.1305.0734,
  title  = {Finite reflection groups and the Dunkl-Laplace differential-difference operators in conformal geometry},
  author = {P. Somberg},
  journal= {arXiv preprint arXiv:1305.0734},
  year   = {2013}
}
R2 v1 2026-06-22T00:11:03.396Z