A Unifying Framework for Complex-Valued Eigenfunctions via The Cartan Embedding

TL;DR

This paper introduces a unifying framework using the Cartan embedding to derive explicit complex-valued eigenfunctions on classical symmetric spaces, also enabling the creation of new eigenfunctions on quaternionic Grassmannians.

Contribution

It provides a unified scheme for eigenfunctions on symmetric spaces and constructs new eigenfunctions on quaternionic Grassmannians using the Cartan embedding.

Findings

Unified scheme for eigenfunctions on classical symmetric spaces

Construction of new eigenfunctions on quaternionic Grassmannians

Enhanced understanding of eigenfunction structures via Cartan embedding

Abstract

In this work we find a unifying scheme for the known explicit complex-valued eigenfunctions on the classical compact Riemannian symmetric spaces. For this we employ the well-known Cartan embedding for those spaces. This also leads to the construction of new eigenfunctions on the quaternionic Grassmannians.