Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-13T05:05:35.774Z Has data issue: false hasContentIssue false
  • English
  • Français

Explicit Forms of Local Lifting for GL2

Published online by Cambridge University Press:  20 November 2018

Donggyun Kim
Donggyun Kim*
Affiliation:
Department of Mathematics, School of Science, Korea University,Seoul 136-701, Koreadkim@semi.korea.ac.kr
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let F be a local non-Archimedean field and let Ꮪ(GL2(F)) be the set of equivalence classes of irreducible admissible representations of GL(F). When K/F be a Galois field extension, there is a map, called lifting, from Ꮪ(GL2(F)) to Ꮪ(GL2(K)). We give an explicit form of lifting when K/F is a quadratic wildly ramified extension and the given representations are Weil supercuspidal. We also provide a comparison between Weil representations and induced representations of GL2(F).

Keywords

22E5011S37
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 48 , Issue 2 , 01 April 1996 , pp. 343 - 362
Copyright
Copyright © Canadian Mathematical Society 1996

References

[BF] Bushnell, C.J. and Frohlich, A., Non-abelian congruence Gauss sums andp-adic simple algebras, Proc. London Math. Soc. (3) 50 (1985), 207–264.Google Scholar
[D1] Deligne, P., Formes modulaires et représentations de GL(2). In: Modular functions of one variable II, Lecture Notes in Math. 349, Springer Verlag, 1979. 55–105.Google Scholar
[D2] Deligne, P., Les constantes des equations functionnelles desJunctions L. In: Modular functions of one variable II, Lecture Notes in Math. 349, Springer Verlag, 1979. 501–597.Google Scholar
[GJ] Godement, R. and Jacquet, H., Zeta functions of simple algebras, Lecture Notes in Math. 260, Springer Verlag, 1972.Google Scholar
[GK] Gérardin, P. and Kutzko, P., Facteurs locauxpour GL(2), Ann. Sci. École Norm. Sup. 13 (1980), 349–384.Google Scholar
[GL] Gérardin, P. and Labesse, J., The solution of a basis change problem for GL(2). In: Automorphic forms, representations, and I-functions, Proc. Symp. Pure Math. XXXIII, Part 2, Amer. Math. Soc, 1979. 115— 133.Google Scholar
[JL] Jacquet, H. and Langlands, R.P., Automorphic forms on GL(2), Lecture Notes in Math. 114, Springer Verlag, 1970.Google Scholar
[H] Henniart, G., Changement de base modéré pour GL(n) sur un corps local, C. R. Acad. Sci. Paris, Serie I 299 (198), 45–48.Google Scholar
[Ho] Howe, R., Some qualitative results on the representation theory of GLn over a p-adic field, Pacific J. Math. 73 (1977), 497–538.Google Scholar
[K1] Kutzko, P., On the supercuspidal representations of GL2I, II, Amer. J. Math. 100( 1978), 43–60. 705-716.Google Scholar
[K2 ] Kutzko, P., The Langlands conjecture for GL(2) of a local field, Ann. of Math. 112 (1980), 381–412.Google Scholar
[K3] Kutzko, P., The exceptional representations of GL2, Compositio Math. 51 (1984), 3–14.Google Scholar
[KM] Kutzko, P. and Moy, A., On the local Langlands conjecture in prime dimension, Ann. of Math. 121 (1985), 495–516.Google Scholar
[L] Langlands, R.P., Base change for GL(2), Ann. of Math. Studies 96, Princeton Univ. Press, 1980.Google Scholar
[M] Moeglin, C., Sur la correspondance de Langlands-Kazhdan, J. Math. Pures Appl. 69 (1980), 175–226.Google Scholar
[N] Nobs, A., Die irreduziblen Darstellungen von GL2(Zp), insbesondere GL2(Z2), Math. Ann. 229 (1977), 113–133.Google Scholar
[P] Pantoja, J., Liftings of supercuspidal representations of GL2 Pacific J. Math. 116 (1985), 307—351.Google Scholar
[S] Serre, J.P., Local fields, Graduate Texts in Math. 67, Springer Verlag, 1979.Google Scholar
[T] Tate, J., Number theoretic background. In: Automorphic forms, representations, and L-functions, Symp. Pure Math. XXXIII, Part 2, Proc. Amer. Math. Soc., 1979. 3–26.Google Scholar
[W] Weil, A., Sur certains groupes d'opérateurs unitaires, Acta Math. 111 (1964), 143–211.Google Scholar
[Z] Zelevinsky, A., Induced representations of reductive p-adic groups II, On irreducible representations of GL(n), Ann. Sci. École Norm. Sup. 13 (1980), 165–210.Google Scholar