Re: the concept of a representation of a group

Thank you for your detailed answer Igor. About the dimension of the
group, I restrict to the case of Lie groups which can be represented by
matrix groups. With the dimension of the group I mean the number of
parameters of the matrix group. What I do not understand is exactly the
relation between the dimension of the group and the dimension of their
representations.

You may mean normal commuting matrices in a), when talking about
simultaneously diagonalizable matrices. You maybe mean in the last
sentence of b), that with help of the natural representation
(forgetting that I do not know what it is exactly) one can find the
fundamental representations, which build up the irreducible
representations by tensor products. I looked regular representation up
in the internet, but I found for SU(n), the regular representation is
the adjoint representation. Is the regular representation the adjoint
representation?

After all my question remains unanswered. Is the dimension of a
representation the dimension of H? Can the quotient group G/ker(f) be
used for something? Maybe you could explain it with the help of a small
simple group, SU(2).

.

Relevant Pages

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