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2009

On Discretization of Tori of Compact Simple Lie Groups

Hrivnak, Jiri, Patera, Jiri

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Three types of numerical data are provided for simple Lie groups of any type and rank.

This data is indispensable for Fourier-like expansions of multidimensional digital data into finite series of $C-$ or $S-$functions on the fundamental domain $F$ of the underlying Lie group $G$.
Firstly, we consider the number $|F_M|$ of points in $F$ from the lattice $P^{\vee}_M$, which is the refinement of the dual weight lattice $P^{\vee}$ of $G$ by a positive integer $M$.
Secondly, we find the lowest set $\Lambda_M$ of dominant weights, specifying the maximal set of $C-$ and $S-$functions that are pairwise orthogonal on the point set $F_M$.

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