×

A simple trace formula. (English) Zbl 0666.10018

A trace formula for automorphic forms of reductive groups is proved for test functions with a single supercuspidal component and another component which is spherical and sufficiently admissible. The resulting formula is used to prove the correspondence of cuspidal modules of \(\mathrm{GL}(n)\) and metaplectic group.

MSC:

11F70 Representation-theoretic methods; automorphic representations over local and global fields
22E55 Representations of Lie and linear algebraic groups over global fields and adèle rings
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bernstein, J.; Deligne, P.; Kazhdan, D.; Vigneras, M.-F., Représentations des groupes réductifs sur un corps local (1984), Paris: Hermann, Paris · Zbl 0544.00007
[2] Bernstein, J.; Zelevinsky, A., Induced representations of reductive p-adic groups I, Ann. Sci. Ec. Norm. Sup., 4e série, 10, 441-472 (1977) · Zbl 0412.22015
[3] Borel, A., Admissible representations of a semi-simple group over a local field with vectors fixed under an Iwahori subgroup, Invent. Math., 35, 233-259 (1976) · Zbl 0334.22012
[4] Borel, A.; Jacquet, H., Automorphic forms and automorphic representations, Proc. Symp. Pure Math., 33, I, 189-208 (1979) · Zbl 0414.22020
[5] Cartier, P., Representations of p-adic groups: A survey, Proc. Symp. Pure Math., 33, I, 111-155 (1979) · Zbl 0421.22010
[6] Casselman, W., Characters and Jacquet modules, Math. Ann., 230, 101-105 (1977) · Zbl 0337.22019
[7] Drinfeld, V., Elliptic modules II, Mat. Sbornik, 102, 2, 159-170 (144) · Zbl 0386.20022
[8] Flicker, Y., Rigidity for automorphic forms, J. Analyse Math., 49, 135-202 (1987) · Zbl 0656.10024
[9] [F′] Y. Flicker,Base change trace identity for U (3), preprint, MSRI (1986); see also:Packets and liftings for U (3), J. Analyse Math.50 (1988), 19-63, this issue. · Zbl 0666.10019
[10] Flicker, Y., Stable base change for spherical functions, Nagoya Math. J., 106, 121-142 (1987) · Zbl 0616.22005
[11] [′F] Y. Flicker,Regular trace formula and base change for GL (n), preprint. · Zbl 0691.10018
[12] [″F] Y. Flicker,Regular trace formula and base change lifting, Am. J. Math., to appear. · Zbl 0666.10020
[13] [′F′] Y. Flicker,On the symmetric square. Total global comparison, preprint. · Zbl 0815.11030
[14] Flicker, Y.; Kazhdan, D., Metaplectic correspondence, Publ. Math. IHES, 64, 53-110 (1987) · Zbl 0616.10024
[15] [FK′] Y. Flicker and D. Kazhdan,Geometric Ramanujan conjecture and Drinfeld reciprocity law, Proc. Selberg Symposium, Oslo, June 1987. · Zbl 0674.10025
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.