On E-Discretization of Tori of Compact Simple Lie Groups

Abstract

Three types of numerical data are provided for compact simple Lie groups $G$ of classical types and of any rank. This data is indispensable for Fourier-like expansions of multidimensional digital data into finite series of $E-$functions on the fundamental domain $F^e$. Firstly, we determine the number $|F_M^e|$ of points in $F^e$ from the lattice $P_M^{\vee }$, which is the refinement of the dual weight lattice $P^{\vee }$ of $G$ by a positive integer $M$. Secondly, we find the lowest set ${\Lambda }_M^e$ of the weights, specifying the maximal set of $E-$functions that are pairwise orthogonal on the point set $F_M^e$. Finally, we describe an efficient algorithm for finding the number of conjugate points to every point of $F_M^e$. Discrete $E-$transform, together with its continuous interpolation, is presented in full generality.

13 pages, 2 figures, revised version

References in corpus (1)

• Antisymmetric Orbit Functions

Cited by in corpus (6)

• On Discretization of Tori of Compact Simple Lie Groups II
• Generalized discrete orbit function transforms of affine Weyl groups
• Weight-Lattice Discretization of Weyl-Orbit Functions
• On E-Discretization of Tori of Compact Simple Lie Groups: II
• Six types of $E-$functions of the Lie groups O(5) and G(2)
• On E-functions of Semisimple Lie Groups