- #1

matematikawan

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I know these definitions:

A representation of a group G is a homomorphism from G to a group of operator on a vector space V. The dimension of the representation is the dimension of the vector V.

If D(g) is a matrix realization of a representation, the character [tex]\chi (g)[/tex] is the trace of D(g).

The paper I'm reading state that the dimension of the representation is the character evaluated on the unit matrix. (***)

I try to confirm this with the character formula for SU(2) which is given as

[tex]\chi^j (\theta)=\frac{\sin(j+\frac{1}{2} )\theta}{\sin \frac{\theta}{2} }[/tex]

where j labelled the irreducible representation.

So at unit matrix [tex]\chi (0) = 2j + 1[/tex] which is the correct dimension for the irreducible representation.

My question is how do we go about proving (***). I can't find the literature that proved this statement. Any clues ?