Compatibility of Local and Global Langlands Correspondences
نویسندگان
چکیده
This paper is a continuation of [HT]. Let L be an imaginary CM field and let Π be a regular algebraic (i.e., Π∞ has the same infinitesimal character as an algebraic representation of the restriction of scalars from L to Q of GLn) cuspidal automorphic representation of GLn(AL) which is conjugate self-dual (Π ◦ c ∼= Π∨) and square integrable at some finite place. In [HT] it is explained how to attach to Π and an arbitrary rational prime l (and an isomorphism ı : Q l ∼ → C) a continuous semisimple representation Rl(Π) : Gal (L/L) −→ GLn(Q l ) which is characterised as follows. For every finite place v of L not dividing l, ıRl(Π)| WLv = rec ( Πv | det | 1−n 2 )ss ,
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