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

## TL;DR

This paper presents a unified approach to complex-valued eigenfunctions on symmetric spaces using the Cartan embedding, enabling the creation of new eigenfunctions on specific spaces.

## Contribution

The paper introduces a novel unifying framework for complex-valued eigenfunctions using the Cartan embedding.

## Key findings

- A unifying scheme for complex-valued eigenfunctions on classical compact Riemannian symmetric spaces is established.
- New eigenfunctions are constructed on the quaternionic Grassmannians using the proposed framework.

## 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.