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New continuous group transforms, together with their discretization over alattice of any density and admissible symmetry, are defined for a generalcompact simple Lie groups of rank $2\leq n<\infty$. Rank 1 transforms areknown. Rank 2 exposition of $C$- and $S$-transforms is in the literature. The$E$-transforms appear here for the first time.

Compact Simple Lie Groups and Their C-, S-, and E-Transforms