Vertical Mirror
is there a difference between finding the characters for a reducible representation of an object and finding?
the characters for an irreducible representation? I think the pattern i notice is that when finding the reducible representation’s character for a vertical mirror plane reflection on something like this :
<-- -->, the character is zero but when doing the vertical mirror plane operation for an irreducible representation, the character might be 2. Hopefully my question makes sense. This is for inorganic chemistry and refering to molecules.
You seem to be a bit confused about what reducible and irreducible representations are (I noticed that in the last question I answered for you too). These are not super difficult concepts to learn, but when I teach a graduate course to inorganic students it takes me several lectures to put these concepts in an understandable context and then to apply them. Basically, reducible representations can have an arbitrarily large dimension, but can be “block-factored” into irreducible representations. If what I mean isn’t entirely clear, perhaps I can help you to more mechanically apply the concepts without going into a more rigorous explanation if you just give an example molecule and a clearly defined example problem. Then I can work out a detailed solution in which I’ll construct the characters of a reducible representation and show which irreducible representations are contained in it.
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