Corpus ID: 118198768

# Direct Systems of Spherical Functions and Representations

@article{Dawson2011DirectSO,
title={Direct Systems of Spherical Functions and Representations},
author={Matthew Dawson and G. {\'O}lafsson and J. Wolf},
journal={arXiv: Representation Theory},
year={2011}
}
• Published 2011
• Mathematics
• arXiv: Representation Theory
• Spherical representations and functions are the building blocks for harmonic analysis on riemannian symmetric spaces. In this paper we consider spherical functions and spherical representations related to certain infinite dimensional symmetric spaces $G_\infty/K_\infty = \varinjlim G_n/K_n$. We use the representation theoretic construction $\phi (x) =$ where $e$ is a $K_\infty$--fixed unit vector for $\pi$. Specifically, we look at representations $\pi_\infty = \varinjlim \pi_n$ of \$G_\infty… CONTINUE READING