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## Main Question or Discussion Point

Hello!

I´m currently reading 'Groups, Representations and Physics' by H.F. Jones and I have drawn some conclusions that I would like to have confirmed + I have some questions. :)

Conclusions:

1. An albelian group has always only one irrep.

2. The direct sum of two representations can be thought of as a matrix on block diagonal form, in which we have one block to each group.

Questions:

1. Jones says that the number of irreps is equal to the numer of conjugacy classes, r = k. But SO(2) is an abelian group so r = 1, but every element is its own conjugacy class since g q g^(-1) = gg^(-1) q = q, so k = infinity?

2. If conclusion 2 is right, how should i think of the matrixrepresentation for a direct product group, say SO(2)xSO(2)?

Maybe some conclusions and questions will be added in the nearby future but this is it for the moment.

Thanks helping!!

// Hymne

I´m currently reading 'Groups, Representations and Physics' by H.F. Jones and I have drawn some conclusions that I would like to have confirmed + I have some questions. :)

Conclusions:

1. An albelian group has always only one irrep.

2. The direct sum of two representations can be thought of as a matrix on block diagonal form, in which we have one block to each group.

Questions:

1. Jones says that the number of irreps is equal to the numer of conjugacy classes, r = k. But SO(2) is an abelian group so r = 1, but every element is its own conjugacy class since g q g^(-1) = gg^(-1) q = q, so k = infinity?

2. If conclusion 2 is right, how should i think of the matrixrepresentation for a direct product group, say SO(2)xSO(2)?

Maybe some conclusions and questions will be added in the nearby future but this is it for the moment.

Thanks helping!!

// Hymne