Explicit harmonic morphisms and $p$-harmonic functions from the complex and quaternionic Grassmannians

TL;DR

This paper constructs explicit $p$-harmonic functions and harmonic morphisms on complex and quaternionic Grassmannians, revealing duality relations and providing tools for analysis on symmetric spaces.

Contribution

It introduces a method to explicitly construct $p$-harmonic functions and harmonic morphisms on classical symmetric Grassmannians using eigenfunctions of specific operators.

Findings

Explicit $p$-harmonic functions on Grassmannians

Harmonic morphisms derived from eigenfunctions

Duality principle linking compact and non-compact spaces

Abstract

We construct explicit complex-valued $p$-harmonic functions and harmonic morphisms on the classical compact symmetric complex and quaternionic Grassmannians. The ingredients for our construction method are joint eigenfunctions of the classical Laplace-Beltrami and the so called conformality operator. A known duality principle implies that these $p$-harmonic functions and harmonic morphisms also induce such solutions on the Riemannian symmetric non-compact dual spaces.