Zonal and Associated Functions on $S{O}_0(p,q)$ Groups

Abstract

Explicit expressions for associated spherical functions of $SO(p,q)$ matrix groups are obtained using a generalized hypergeometric series of two variables. In this paper, we present explicit expressions for zonal functions of de Sitter groups and the group of conformal invariance. Moreover, we present a theorem on the transformation of derivative of distributions, concentrated on smooth surfaces, with respect to infinite-dimensional Lie group $C^{\infty }\left({\mathbb{R}}^n,GL(n)\right)$.

12 pages. arXiv admin note: substantial text overlap with arXiv:math-ph/0303058

References in corpus (2)

• Zonal Functions on $SO(p,q)$ Groups
• Associated functions on $SO(p,q)$ Groups