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Jul 30, 2019 at 12:19 vote accept M. Winter
Jul 30, 2019 at 12:18 comment added Derek Holt Yes, the primitive permutation representation of degree $91$ of ${\rm PSL}(2,13)$ has a repeated real constituent of degree $13$.
Jul 29, 2019 at 15:58 comment added M. Winter Thank you for this nice example. I am indeed mainly interested in real irreducible represenations, so this fits perfectly. Do you see any immediate reason why the dimension of such an irreducible representation of multiplicity $\ge 2$ has to be even? I would be highly interested in an example of odd dimension if you know of one.
Jul 29, 2019 at 14:00 history answered Derek Holt CC BY-SA 4.0