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## Main Question or Discussion Point

For a specific wave vector, ##k##, the group of wave vector is defined as all the space group operations that leave ##k## invariant or turn it into ##k+K_m## where ##K_m## is a reciprocal vector. How the translation parts of the space group, ##\tau##, can act on wave vector? Better to say, the dimension of a wave vector is ##1/length## while the translation operator acts on the lengths!