17 citations · 18 across the 3 of their papers we have counts for
6 papers
Nested polyhedra and indices of orbits of Coxeter groups of non-crystallographic type
Mariia Myronova, Jiri Patera, Marzena Szajewska
The invariants of finite-dimensional representations of simple Lie algebras, such as even-degree indices and anomaly numbers, are considered in the context of the non-crystallograp…
Group theoretical methods to construct the graphene
Zofia Grabowiecka, Jiri Patera, Marzena Szajewska
In this paper, the tiling of the Euclidean plane with regular hexagons whose vertices are occupied by carbon atoms is called the graphene. We describe six different ways to generat…
Dominant weight multiplicities in hybrid characters of Bn, Cn, F4, G2
Francis W. Lemire, Jiri Patera, Marzena Szajewska
The characters of irreducible finite dimensional representations of compact simple Lie group G are invariant with respect to the action of the Weyl group W(G) of G. The defining pr…
Faces of platonic solids in all dimensions
Marzena Szajewska
This paper considers Platonic solids/polytopes in the real Euclidean space R^n of dimension 3 <= n < infinity. The Platonic solids/polytopes are described together with their faces…
Four types of special functions of G_2 and their discretization
Marzena Szajewska
Properties of four infinite families of special functions of two real variables, based on the compact simple Lie group G2, are compared and described. Two of the four families (cal…
Orthogonal polynomials of compact simple Lie groups: Branching rules for polynomials
Maryna Nesterenko, Jiri Patera, Marzena Szajewska +1
Polynomials in this paper are defined starting from a compact semisimple Lie group. A known classification of maximal, semisimple subgroups of simple Lie groups is used to select t…