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I am looking for a list of the irreducible representations of O(2). Could someone please provide a reference?

EDIT: I am particularly interested in the representations on IR^2 (irreducible or not)

edited Sep 2 2010 at 14:06

asked Sep 2 2010 at 9:22

Orbicular
1,794●8●18

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Real or complex? – S. Carnahan♦ Sep 2 2010 at 12:00

For SO(n,C), see Theorem 2 here: books.google.com/… – mathphysicist Sep 2 2010 at 13:02

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If you are interested in complex irreps, then the book mentioned in the (deleted) answer by mathphysicist has the answer: it is Theorem 11.3, except that as stated the theorem is not right because it fails to mention that this is true for complex irreps. – José Figueroa-O'Farrill Sep 2 2010 at 13:51

@mathphysicist: I would undelete your answer and simply point out the above "caveat". – José Figueroa-O'Farrill Sep 2 2010 at 13:52

@Jose: I've just undeleted the answer. – mathphysicist Sep 2 2010 at 15:14

mathphysicist · Answer 1 · 2010-09-02 15:10:45Z UTC

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You can look into this section of the book Group theory in physics by Wu-Ki Tung to begin with.

EDIT: Theorem 11.3 from this book works for complex irreps only (see Jose's comments to the answer and to the question).

edited Sep 2 2010 at 15:10

answered Sep 2 2010 at 9:32

mathphysicist
3,506●14●29

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This books contains the assertion that all irreps of SO(2) are one-dimensional. So reader beware... – José Figueroa-O'Farrill Sep 2 2010 at 10:57

@Jose: Thanks for pointing this out. I guess I'd then better remove my answer. – mathphysicist Sep 2 2010 at 12:49

@Jose: I hope the answer is OK now. If it isn't, please feel free to correct me. – mathphysicist Sep 2 2010 at 15:11

irreducible representations of O(2) - reference?

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