Orbit spaces of Weyl groups acting on compact tori: a unified and explicit polynomial description

DOI10.1137/23m158173xMaRDI QIDQ6594419

Evelyne Hubert, Tobias Metzlaff, Cordian Riener

Publication date: 28 August 2024

Published in: SIAM Journal on Applied Algebra and Geometry (Search for Journal in Brave)

zbMATH Keywords

Weyl groupsChebyshev polynomialsroot systemsmultiplicative invariantssemi-algebraic setsorbit spacespolynomial matrix inequalities

Mathematics Subject Classification ID

Actions of groups on commutative rings; invariant theory (13A50) Semialgebraic sets and related spaces (14P10) Orthogonal polynomials and functions associated with root systems (33C52) Root systems (17B22)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Discrete Fourier analysis and Chebyshev polynomials with \(G_{2}\) group
• Spectral bounds for the independence ratio and the chromatic number of an operator
• Cubature formulae for orthogonal polynomials in terms of elements of finite order of compact simple Lie groups
• Multiplicative invariants
• Discrete Fourier analysis on fundamental domain and simplex of \(A_{d}\) lattice in \(d\)-variables
• Inequalities defining orbit spaces
• Multi-dimensional generalizations of the Chebyshev polynomials. I
• A class of orthogonal polynomials in \(k\) variables
• On a theorem of Pittie
• Positive symmetric functions
• Multiplicative invariant theory
• Sparse interpolation in terms of multivariate Chebyshev polynomials
• Generating formulas for finite reflection groups of the infinite series \(S_n\), \(A_n\), \(B_n\) and \(D_n\)
• Global optimization with polynomials and the problem of moments
• Discrete Fourier Analysis, Cubature, and Interpolation on a Hexagon and a Triangle
• Chebyshev Polynomials in Several Variables and the Radial Part of the Laplace-Beltrami Operator
• Lasserre Hierarchy for Large Scale Polynomial Optimization in Real and Complex Variables
• Using Algebraic Geometry
• Generalized Chebyshev Polynomials Associated with Affine Weyl Groups
• Semidefinite Optimization and Convex Algebraic Geometry
• Ideals, Varieties, and Algorithms
• Generalized Characteristic Polynomials and Gaussian Cubature Rules
• Positive trigonometric polynomials and signal processing applications
• T-orbit spaces of multiplicative actions and applications

This page was built for publication: Orbit spaces of Weyl groups acting on compact tori: a unified and explicit polynomial description