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Jul 9, 2016 at 15:37 comment added benblumsmith +1 This whole discussion is just what I needed.
Jul 9, 2016 at 9:30 comment added Qiaochu Yuan @Derek: you're right. So in fact it's unnecessary to know anything about the irreducibles over $\mathbb{R}$.
Jul 9, 2016 at 8:28 comment added Derek Holt So isn't the simple answer that you calculate its (complex) character, decompose it into irreducibles, and check whether it is the sum of pairs of conjugate characters?
Jul 9, 2016 at 7:07 vote accept benblumsmith
Jul 9, 2016 at 1:21 history answered Qiaochu Yuan CC BY-SA 3.0