Quasi-invariants of dihedral systems

TL;DR

This paper constructs an explicit basis of quasi-invariants for two-dimensional Coxeter systems with arbitrary multiplicities, generalizing previous results for constant multiplicities by demonstrating these basis elements are m-harmonic polynomials.

Contribution

It provides an explicit basis of quasi-invariants for dihedral systems with arbitrary multiplicities, extending earlier work on constant multiplicity cases.

Findings

Explicit basis of quasi-invariants constructed

Basis elements are m-harmonic polynomials

Generalization of Veselov's earlier results

Abstract

A basis of quasi-invariant module over invariants is explicitly constructed for the two-dimensional Coxeter systems with arbitrary multiplicities. It is proved that this basis consists of $m$-harmonic polynomials, thus the earlier results of Veselov and the author for the case of constant multiplicity are generalized.