Extremal polynomials in stratified groups

TL;DR

This paper introduces extremal polynomials linked to stratified nilpotent Lie algebras, providing an algebraic approach to abnormal subriemannian geodesics and enabling integration of adjoint equations.

Contribution

It presents a new family of extremal polynomials and their structure relations, offering a novel algebraic characterization of abnormal geodesics in stratified nilpotent Lie groups.

Findings

Defined extremal polynomials for stratified Lie algebras

Established structure relations for these polynomials

Applied to integrate adjoint equations in subriemannian geometry

Abstract

We introduce a family of extremal polynomials associated with the prolongation of a stratified nilpotent Lie algebra. These polynomials are related to a new algebraic characterization of abnormal subriemannian geodesics in stratified nilpotent Lie groups. They satisfy a set of remarkable structure relations that are used to integrate the adjoint equations.