The paper develops applications of symmetric orbit functions, known from irreducible
representations of simple Lie groups, in numerical analysis. It is shown that these functions …

A finite group with an integer representation has a multiplicative action on the ring of Laurent
polynomials, which is induced by a nonlinear action on the compact torus. We study the …

Résumé Cette these étudie le probleme de l'optimisation d'un polynôme trigonométrique
avec symétrie cristallographique. L'optimisation des polynômes trigonométriques était l'objet …

The discrete cosine transforms of types V--VIII are generalized to the antisymmetric and
symmetric multivariate discrete cosine transforms. Four families of discretely and …

The generating functions of fourteen families of generalized Chebyshev polynomials related
to rank two Lie algebras A 2, C 2 and G 2 are explicitly developed. There exist two classes of …

The aim of this article is to describe several cubature formulas related to the Weyl group orbit
functions, ie to the special cases of the Jacobi polynomials associated to root systems. The …

Consider a finite collection of classical point charges constrained on the surface of a
conductor and interacting through a Coulomb potential. In the absence of other forces …

We develop lower bounds for the energy of configurations in $\mathbb {R}^ d $ periodic with
respect to a lattice. In certain cases, the construction of sharp bounds can be formulated as a …

The Weyl group of a crystallographic root system has a multiplicative action on the compact
torus. The orbit space of this action is a compact basic semi-algebraic set. We present a …

We note a remarkable similarity between the discretized Weyl-orbit functions and affine
modular data associated with Wess–Zumino–Novikov–Witten (WZNW) conformal field …