Gelfand-Tsetlin Bases of Orthogonal Polynomials in Hermitean Clifford Analysis

TL;DR

This paper presents an explicit algorithm for constructing orthogonal bases of homogeneous polynomials within Hermitean Clifford analysis, a higher-dimensional function theory involving complex Dirac operators.

Contribution

It introduces a novel explicit algorithmic method for orthogonal basis construction in Hermitean Clifford analysis, advancing the understanding of polynomial spaces in this context.

Findings

Explicit algorithm for orthogonal basis construction

Application to spaces of homogeneous polynomials

Enhancement of Hermitean Clifford analysis techniques

Abstract

An explicit algorithmic construction is given for orthogonal bases for spaces of homogeneous polynomials, in the context of Hermitean Clifford analysis, which is a higher dimensional function theory centred around the simultaneous null solutions of two Hermitean conjugate complex Dirac operators.