Regular trace formula and base change for GL(n)
Annales de l'Institut Fourier, Tome 40 (1990) no. 1, pp. 1-30.

La formule de trace “régulière” pour une fonction avec une composante locale qui est bi-invariante par un sous-groupe d’Iwahori et suffisamment régulière par rapport aux autres composantes, est développée dans le contexte d’un groupe réductif. On l’utilise pour donner une démonstration élémentaire de la théorie des changements des bases pour les représentations automorphes cuspidales de GL(n) qui ont une composante supercuspidale. On donne aussi une preuve locale du transfert des intégrales orbitales de fonctions locales générales, qui est au contraire obtenu comme corollaire de la correspondance locale.

The “regular”trace formula, for a test function with a local component which is Iwahori-biinvariant and sufficiently regular with respect to the other components, is developed in the context of a reductive group. It is used to give a simple proof of the theory of base-change for cuspidal automorphic representations of GL(n) which have a supercuspidal component. A purely local proof is given to transfer orbital integrals of sufficiently many spherical functions, by relating them to regular Iwahori functions. Transfer of orbital integrals of smooth functions is not used in the proof. Instead it is obtained as a corollary to the local lifting.

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Flicker, Yuval Z. Regular trace formula and base change for $GL(n)$. Annales de l'Institut Fourier, Tome 40 (1990) no. 1, pp. 1-30. doi : 10.5802/aif.1201. http://www.numdam.org/articles/10.5802/aif.1201/

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