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I do not really understand the intuition behind the functions assigned to irreducible representations. For example, in H₂O, the A₂ representation is given by

E   C₂   σv(xz)   σv(yz)
1   -1    1       -1

and the associated linear functions are x and Ry, but I am not sure where these come from.

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  • $\begingroup$ Since 5 months have gone by with no answers or comments, I think it's fair to let you know about Matter Modeling Stack Exchange which also answers group theory questions, but make sure to delete the question from here if you're cross-posting there (or to at least put a note at the top of your question, saying that it's cross-posted). $\endgroup$ Commented Aug 8, 2023 at 2:25

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