# Jiří Hrivnák

## Honeycomb Weyl orbit functions of $G_2$

Motivated by current extensive research of triangular graphene quantum dots, the two-dimensional honeycomb lattice is constructed via subtraction of the weight and dual weight lattices of the crystallographic root system $G_2$. Four types of Weyl orbit functions, that correspond to four sign homomorphisms of the associated Weyl group, are labelled by the dominant weights from the weight lattice. The fundamental and dual fundamental domains of the induced affine and dual affine Weyl groups determine both finite point and weight sets utilized for simultaneous weight and dual weight discretizations of Weyl orbit functions. Modified weight sets of the dual weight discretization represent cornerstones for introduction of $G_2$ honeycomb Weyl orbit functions. Subtracting the weight and dual weight point sets produces honeycomb point sets shaped as 30-60-90 triangles over which the discrete orthogonality of honeycomb Weyl orbit functions is discussed. This is a joint work with Tomasz Czyżycki.