Explicit proper p-harmonic functions on the Riemannian symmetric spaces SU(n)/SO(n), Sp(n)/U(n), SO(2n)/U(n), SU(2n)/Sp(n)

TL;DR

This paper constructs explicit complex-valued p-harmonic functions on certain compact Riemannian symmetric spaces and discusses their counterparts on non-compact dual spaces.

Contribution

It provides explicit formulas for p-harmonic functions on specific symmetric spaces and extends the construction to their non-compact duals.

Findings

Explicit p-harmonic functions on SU(n)/SO(n), Sp(n)/U(n), SO(2n)/U(n), SU(2n)/Sp(n)

Construction methods for functions on dual spaces

Extension of functions to non-compact symmetric spaces

Abstract

In this work we construct explicit complex-valued p-harmonic functions on the compact Riemannian symmetric spaces SU(n)/SO(n), Sp(n)/U(n), SO(2n)/U(n), SU(2n)/Sp(n). We also describe how the same can be manufactured on their non-compact symmetric dual spaces.