XXIX Workshop on Geometric Methods in Physics 27.06-03.07.2010

Jiří Hrivnák

E-Discretization of Tori of Exceptional Compact Simple Lie Groups

We consider an exceptional compact simple Lie group $G$, the corresponging affine Weyl group and its even subgroup. Given a positive integer $M$ we introduce a finite set of lattice points $F^e_M$. The even affine Weyl group determines the symmetry of the grid $F^e_M$, the number $M$ determines its density . We present a construction of the set $F^e_M$ and explicitly count the numbers of its points for the cases of $G_2$ and $F_4$. We specify the maximal set of pairwise orthogonal $E-$functions over $F^e_M$. This finite set allows us to calculate Fourier like discrete expansions of arbitrary discrete function on $F^e_M$.

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