3-characterizations of finite groups by Podufalov N. D.

By Podufalov N. D.

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I) to me by H a r i s h - C h a n d r a . A weaker as s t a t e d See Chapter in the p - a d i c case. So o n c e all series representations are irreducible. is k n o w n about the r e d u c i b l e EXERCISE, groups For ones G = SL(n,~), (~ ;) P = [] are [] than in the m i n i m a l compute cuspidal, which and w r i t e again C 5 almost Much less case. of the down actually V, T h e o r e m version principal version here for a c o r r e s p o n d i n g these T ( A. : o(m) T(a). as we qp correspond- can be r e a l i z e d to the r e a d e r q-function information (o • representations left is a f i n i t e finite given K/Kn M 7 ~(O,T), appears and Then G/P).

I) also was q x T. told The as P These both are the M ~ /E exactly as in the m i n i - (for m o r e prgncipaZ serges follows. Let by and ~N o e Md' that did in the m i n i - as an e x e r c i s e gives the q u a s i - ~(~(OI,TI),~(O2,T2)) appears ~ #s s(o x ~) ~ o x T. s ( W A. in H a r i s h - C h a n d r a there. ~ WA: That result [ii]. (i) to me by H a r i s h - C h a n d r a . A weaker as s t a t e d See Chapter in the p - a d i c case. So o n c e all series representations are irreducible.

The ~ x~, representations ~ r M, }. The characters GH and on the set M = , of t h e s e Hv set of the princi- T c A, representations are given by the are formu- las @o r e ( h ) = laliP+ ' if T ca0 0 fact = a Ip , o compact ~(o,T) discrete Cartan parameterized by but except B) w e r e supported @+-(h) n representations down and (e 0 O+(b) e ~ i ~ ( -=l ++(e 2 n ) in ~ ) e_i~- , _ the Plancherel as follows: fG I f ( g ) 1 2 d g For = G B. b : formula a suitable n>l n~N~, of (n-89 G The The the (true) fact (corresponding B2.

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