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Apr 29, 2018 at 7:52 comment added Vít Tuček These unitary representations are for $SU(p,q)$. I don't know whether they are faithful but since they can be realized as (kernels of differential operators acting on) holomorphic functions on bounded symmetric domains I am inclined to believe that they are.
Apr 27, 2018 at 18:56 comment added მამუკა ჯიბლაძე Do any of these also answer 3.? That is, provide faithful representations for the universal covers of general linear groups?
Apr 27, 2018 at 18:40 history answered Vít Tuček CC BY-SA 3.0