# Group of a wave vector

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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!

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You are using the word space in space group as physical space. You can have space group symmetries without having dimensions of length.

Your question makes me wonder if you know what a wave vector looks like in reciprocal space and what it represents in a wave function.

You are using the word space in space group as physical space. You can have space group symmetries without having dimensions of length.

Your question makes me wonder if you know what a wave vector looks like in reciprocal space and what it represents in a wave function.
I don't know about that. Could you please help me with how a translation operator $\tau$ act on a wave vector $k$?