Vojtěch Teska
Splitting of discrete Weyl orbit function transforms in the root system $A_3$
Irreducible crystallographic root systems and their corresponding Weyl groups determine invariant lattices which serve as the basis of discrete Fourier-like transforms. A finite fragment of a shifted invariant lattice located in the fundamental domain of a generalized affine Weyl group plays the role of the time domain signal while the finite frequency basis consists of Weyl orbit functions labeled by elements of the weight lattice.
Recently developed general theory of these transforms is used to decompose the original point set into smaller subsets, called splitting point sets, which allow a different transform to be carried out. The relationship between corresponding Fourier coefficients will be described and an example in the root system $A_3$ will be presented.
