By Theorem 3, L2(G′1(k)\G0) ∼= L2(G′2(k)\G0) as representation spaces, so the result follows.
Let us now define a map JL0, which takes an irreducible infinitedimensional sub-representation π′′ of L2(Δ\G0) to an irreducible infinitedimensional sub-representation π of L2(G(k)\G(A)), which occurs in [AT] E. Artin and J. Tate, Class Field Theory, W.A. Benjamin, 1967.
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