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as the title, I want to know the complex representations of the $B(2，\overline{\mathbb{F}_p})$, i.e. invertible upper triangle matrix groups over $\mathbb{F}_p$'s algebraic closure $\overline{\mathbb{F}_p}$...

I know some irreducible representations of this group which can be constructed through Mackey method(B=AH...). But I do not know whether these irreducible representations are the whole irreducible representations. The original Mackey's method was established for finite groups， I don't know whether it can be extended to infinite groups.

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  • $\begingroup$ and what is $B(2,F)$ ? And what is the Mackey method you mention - provide a reference... $\endgroup$
    – Dima Pasechnik
    Commented Apr 30, 2015 at 9:04
  • $\begingroup$ B(F) means the subgroup of GL(F) consisting of upper triangle matrix. 2 is matrix's order. And as for Mackey method, it is in Linear Representations of Finite Groups J.P Serre, Chapter 8.2: assume A( Abelian and normal), H are 2 subgroups of G, then the representations of G can be gotten from the representations of A and H. $\endgroup$
    – R Young
    Commented Apr 30, 2015 at 9:21

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