|XXXV Workshop on Geometric Methods in Physics
Weight- and Coweight-Lattice Discretization of Weyl-Orbit Functions
It is standard to perform the discrete Fourier analysis with Weyl-orbit functions on the coweight-lattice fragment contained in the fundamental region of the affine Weyl group. Here we compare the standard treatment to the recently-developed analysis on the fragment of the weight lattice. The weight-lattice discretization possesses symmetry between the labels and the arguments of the Weyl-orbit functions. This property allows the construction of unitary, symmetric matrices with Weyl-orbit-valued elements. For antisymmetric orbit functions, these matrices coincide with the Kac-Peterson modular $S$ matrices. Consequences of the weight lattice discretization for the corresponding orthogonal polynomials are also discussed. This is a joint work with Mark Walton.