Timeline for For a representation V of a finite group G, when is Hom(W, W⊗V) trivial for all irreps W?
Current License: CC BY-SA 2.5
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| Apr 25, 2010 at 23:08 | comment | added | Theo Johnson-Freyd | @QY: I must have misunderstood the question. Oh, I see: I missed the words "if G is a finite subgroup of" and thought you were ust interested in the representation theory of SU(2). My bad. | |
| Apr 25, 2010 at 21:17 | comment | added | Noah Snyder | Yes, when wt(V) is in Q it's automatically a summand of something of the form WW*. For one proof see Claim on the bottom of page 17 of arxiv.org/abs/0810.0084 There's an interesting related result about fusion categories having a "universal grading group" whose trivial part is exactly the summands of WW* see arxiv.org/abs/math/0610726 | |
| Apr 25, 2010 at 21:13 | comment | added | Qiaochu Yuan | I think you're answering a different question than I'm posing. How is highest weight theory applicable to finite group representations? | |
| Apr 25, 2010 at 20:46 | history | answered | Theo Johnson-Freyd | CC BY-SA 2.5 |