Hypergroup properties for the deltoid model

TL;DR

This paper explores the hypergroup property of orthogonal polynomials linked to the deltoid curve and G2 root system, expanding understanding of algebraic structures in mathematical analysis.

Contribution

It establishes the hypergroup property for polynomial families associated with the deltoid curve and G2 root system, revealing new algebraic insights.

Findings

Hypergroup property proven for deltoid curve polynomials

Extension of hypergroup property to G2 root system polynomials

Enhanced understanding of algebraic structures in orthogonal polynomials

Abstract

We investigate the hypergroup property for the family of orthogonal polynomials associated with the deltoid curve in the plane, related to the A 2 root system. This provides also the same property for another family of polynomials related to the G 2 root system.