Jacquet modules of locally analytic representations of $p$-adic reductive groups I. Construction and first properties

Emerton, Matthew

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 39 (2006) no. 5, pp. 775-839.

[1] Ash A., Stevens G., p-Adic deformations of arithmetic cohomology, Preprint. | MR

[2] Bosch S., Güntzer U., Remmert R., Non-Archimedean Analysis, Springer, Berlin, 1984. | MR | Zbl

[3] Bourbaki N., Elements of Mathematics. Topological Vector Spaces, Springer, Berlin, 1987, (Chapters 1-5). | MR | Zbl

[4] Cartier P., Representations of $p$-adic groups: A survey, in: Automorphic Forms, Representations, and L-Functions, Part 1, Proc. Symp. Pure Math., vol. 33, Amer. Math. Soc., Providence, RI, 1979, pp. 111-155. | MR | Zbl

[5] Casselman W., Introduction to the theory of admissible representations of p-adic reductive groups, unpublished notes distributed by P. Sally, draft dated May 7, 1993. Available electronically at, http://www.math.ubc.ca/people/faculty/cass/research.html.

[6] Coleman R., P-adic Banach spaces and families of modular forms, Invent. Math. 127 (1997) 417-479. | MR | Zbl

[7] Coleman R., Mazur B., The eigencurve, in: Scholl A.J., Taylor R.L. (Eds.), Galois Representations in Arithmetic Algebraic Geometry (Durham, 1996), London Math. Soc. Lecture Note Ser., vol. 254, Cambridge University Press, Cambridge, 1998, pp. 1-113. | MR | Zbl

[8] Emerton M., Locally analytic vectors in representations of locally p-adic analytic groups, Mem. Amer. Math. Soc., in press. Available electronically at, http://www.math.northwestern.edu/~emerton.

[9] Emerton M., On the interpolation of systems of eigenvalues attached to automorphic Hecke eigenforms, Invent. Math. 164 (2006) 1-84. | MR | Zbl

[10] Emerton M., Locally analytic representation theory of p-adic reductive groups: A summary of some recent developments, in: Burns D., Buzzard K., Nekovar J. (Eds.), Proceedings of a Symposium on L-Functions and Galois Representations (Durham, 2004), in press. Available electronically at, http://www.math.northwestern.edu/~emerton. | Zbl

[11] Emerton M., Jacquet modules of locally analytic representations of p-adic reductive groups II. The relation to parabolic induction, in preparation.

[12] Féaux de Lacroix C.T., Einige Resultate über die topologischen Darstellungen p-adischer Liegruppen auf unendlich dimensionalen Vektorräumen über einem p-adischen Körper, Thesis, Köln 1997, Schriftenreihe Math. Inst. Univ. Münster, 3. Serie, Heft 23, 1999, pp. 1-111. | MR | Zbl

[13] Knapp A.W., Representation Theory of Semisimple Groups. An Overview Based on Examples, Princeton University Press, Princeton, NJ, 1986. | MR | Zbl

[14] Prasad D., Locally algebraic representations of p-adic groups, Appendix to [18], Represent. Theory 5 (2001) 125-127. | MR

[15] Schneider P., Nonarchimedean Functional Analysis, Springer Monographs in Math., Springer, Berlin, 2002. | MR | Zbl

[16] Schneider P., Teitelbaum J., p-adic boundary values, Astérisque 278 (2002) 51-123. | Numdam | MR | Zbl

[17] Schneider P., Teitelbaum J., Locally analytic distributions and p-adic representation theory, with applications to ${\mathrm{GL}}_2$, J. Amer. Math. Soc. 15 (2001) 443-468. | MR | Zbl

[18] Schneider P., Teitelbaum J., $U\left(g\right)$-finite locally analytic representations, Represent. Theory 5 (2001) 111-128. | MR | Zbl

[19] Schneider P., Teitelbaum J., Banach space representations and Iwasawa theory, Israel J. Math. 127 (2002) 359-380. | MR | Zbl

[20] Schneider P., Teitelbaum J., Algebras of p-adic distributions and admissible representations, Invent. Math. 153 (2003) 145-196. | MR | Zbl

[21] Serre J.-P., Endomorphismes complètement continus des espaces de Banach p-adiques, Publ. Math. IHÉS 12 (1962) 69-85. | EuDML | Numdam | MR | Zbl

[22] Serre J.-P., Lie Algebras and Lie Groups, W.A. Benjamin, 1965. | MR | Zbl