Download Automorphic forms, representations, and L-functions, Part 2 by Armand Borel, W. Casselman (editors) PDF

By Armand Borel, W. Casselman (editors)

Complaints of Symposia in natural arithmetic

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Additional resources for Automorphic forms, representations, and L-functions, Part 2

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56 1 8 . Relations with other types of £-functions . . . . . . . . . . . . . . . . . . . . 58 References 59 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48 IV. The L-function of an automorphic representation . . . . . . . . . . . . . . . . . 49 13. 49 14. The £-function of an automorphic representation . . . . . . . . . . . . . . 5 2 V. Lifting problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 1 5. £-homomorphisms of L-groups . . . . . . . .

LG' and Lp(LG') =:J Lp(LG) ; therefore a e l/J(G) = a e l/J(G'). 4. PROPOSITION. finite separable extension of k; let G' be a connected reductive k-group and G = Rk'lk G' . ::, l/J(G'). 2) : Moreover LGo = = rk, A' = rk'• B = w;, B' = W� , . (LG'0) (see 5. 2 : fll( w� ; LG0) ____::::____, fll( w�, ; LG'0) , But it is clear that this isomorphism maps l/J(G) onto l/J(G'). 5. Let ZL = C(LG0). _. a(w)b(w) is again a 1 -cocycle of W� in LG0• If a is continuous and b cor­ responds to (/) e l/J(G), then ab corresponds to an element of l/J(G).

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