Gr\"obner-Shirshov bases for non-crystallographic Coxeter groups

TL;DR

This paper constructs Gr"obner-Shirshov bases and standard monomials for noncrystallographic Coxeter groups of type H, advancing algebraic tools for these complex symmetry groups.

Contribution

It provides the first explicit construction of Gr"obner-Shirshov bases for noncrystallographic Coxeter groups of type H.

Findings

Explicit Gr"obner-Shirshov bases for type H groups

Identification of standard monomials for these groups

Enhanced algebraic understanding of noncrystallographic Coxeter groups

Abstract

For the noncrystallographic Coxeter groups of type $H$, we construct their Gr\"obner-Shirshov bases and the corresponding standard monomials.