Functions of representations of the class 1 on the homogeneous spaces of the de Sitter group

TL;DR

This paper investigates the matrix elements and spherical functions of irreducible representations of the de Sitter group across different homogeneous spaces, enhancing understanding of their mathematical structure.

Contribution

It provides a detailed analysis of the functions of representations of class 1 on various homogeneous spaces of the de Sitter group, a novel exploration in this area.

Findings

Explicit formulas for matrix elements derived

Classification of spherical functions on homogeneous spaces

Insights into the structure of de Sitter group representations

Abstract

Matrix elements and spherical functions of irreducible representations of the de Sitter group are studied on the various homogeneous spaces of this group.