Examining the C3v character table. I explain how to obtain the irreducible representations from the matrix representations, how the irreducible representations form a group, the E Mulliken symbol, and how the C3v symmetry operations influence functions such as f(x)=x, f(y)=y, f(z)=z, and the rotations.

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References

Symmetry: An Introduction to Group Theory and its Applications by Roy McWeeny
https://www.amazon.com/Symmetry-Intro...