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I'm studying group theory and I'm dealing with irreducible representations (irreps) of C3v. Now since C3v is invariant after 6 simmetry operations I expect, as a consequence of the well known relationship g=Sum_i n^2_i (where g is the order of the group and n_i is the size of the matrices corresponding the i-th irrep), to have 2 irreps of dimension 1 and 1 irrep of dimension 2. This 3 irreps are found to be named A1, A2 (1-dimensional) and E (2-dimensional). There are examples of functions transforming as the A1 and E irreps (for example the pz orbital in the ammonia molecule transforms as A1, while px and py mix up following the rules of E). Similarly s-orbitals and d-orbitals transform as A1 and E, but I have not found so far an example of a function transforming as the 1-dim A2.

It therefore seems to me that there are irreps that have a profound physical meaning such as A1 and E irreps for c3v, being closely associated with the properties of transformation of orbitals, and others, like A2, having less physical meaning.

Do you agree? Could you please comment?

Thanks a lot,

R.Gaspari

PS is it possible to use latex formulae?

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# Irreducible representation of C3v

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