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S Mar 28 at 4:04 history bounty ended CommunityBot
S Mar 28 at 4:04 history notice removed CommunityBot
S Mar 20 at 2:51 history bounty started John Rached
S Mar 20 at 2:51 history notice added John Rached Authoritative reference needed
Mar 17 at 8:14 comment added YCor It is an observation of A. Rapinchuk (Proc AMS 1997, link to AMS site) that for a Kazhdan group, every finite-dimensional unitary rep is conjugate to one that is valued in a number field. I don't exactly know if this is enough to deduce the negative of what you expect, when the character is not valued in any number field.
Mar 17 at 8:08 history edited YCor CC BY-SA 4.0
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Mar 17 at 1:09 history asked John Rached CC BY-SA 4.0