We know that some representation may be reducible, but how can we find out whether it is full reducible. If we can reduce the representation into some lower dimension, it’ll be very helpful for our to discuss specific groups. Fortunately, we find that unitary group will be full reducible or irreducible. And the unitary group […]

## Group Theory 3.1 Representation

Gist Representation is just a homomorphism mapping (1) where is an operator on linear vector space , such that (2) Dimension of the representation: is the dimension of the vector space . Faithful: If the homomorphism is also an isomorphism. Degenerate representation: The one which is not Faithful. Matrix Representation: is the case […]

## Group Theory 3.2 Irreducible, Inequivalent Representation

We can use group representation to discuss group as it’s said in section 3.1 now. But there may be so many representation, which one will be the simple one without erasing the details of the group. This section is to discuss the simplicity.

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