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Locally analytic vectors in representations of locally $p$-adic analytic groups
About this Title
Matthew Emerton
Publication: Memoirs of the American Mathematical Society
Publication Year:
2017; Volume 248, Number 1175
ISBNs: 978-0-8218-7562-9 (print); 978-1-4704-4052-7 (online)
DOI: https://doi.org/10.1090/memo/1175
Published electronically: February 1, 2017
Table of Contents
Chapters
- Introduction
- 1. Non-archimedean functional analysis
- 2. Non-archimedean function theory
- 3. Continuous, analytic, and locally analytic vectors
- 4. Smooth, locally finite, and locally algebraic vectors
- 5. Rings of distributions
- 6. Admissible locally analytic representations
- 7. Representations of certain product groups
- Pierre Berthelot, ${\scr D}$-modules arithmĂ©tiques. I. OpĂ©rateurs diffĂ©rentiels de niveau fini, Ann. Sci. Ăcole Norm. Sup. (4) 29 (1996), no. 2, 185â272 (French, with English summary). MR 1373933
- Armand Borel, Linear algebraic groups, W. A. Benjamin, Inc., New York-Amsterdam, 1969. Notes taken by Hyman Bass. MR 0251042
- S. Bosch, U. GĂŒntzer, and R. Remmert, Non-Archimedean analysis, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 261, Springer-Verlag, Berlin, 1984. A systematic approach to rigid analytic geometry. MR 746961
- Siegfried Bosch and Werner LĂŒtkebohmert, Formal and rigid geometry. II. Flattening techniques, Math. Ann. 296 (1993), no. 3, 403â429. MR 1225983, DOI 10.1007/BF01445112
- N. Bourbaki, Topological vector spaces. Chapters 1â5, Elements of Mathematics (Berlin), Springer-Verlag, Berlin, 1987. Translated from the French by H. G. Eggleston and S. Madan. MR 910295
- Christophe Breuil, Invariant $\scr L$ et sĂ©rie spĂ©ciale $p$-adique, Ann. Sci. Ăcole Norm. Sup. (4) 37 (2004), no. 4, 559â610 (French, with English and French summaries). MR 2097893, DOI 10.1016/j.ansens.2004.02.001
- R. Coleman and B. Mazur, The eigencurve, Galois representations in arithmetic algebraic geometry (Durham, 1996) London Math. Soc. Lecture Note Ser., vol. 254, Cambridge Univ. Press, Cambridge, 1998, pp. 1â113. MR 1696469, DOI 10.1017/CBO9780511662010.003
- Matthew Emerton, Jacquet modules of locally analytic representations of $p$-adic reductive groups. I. Construction and first properties, Ann. Sci. Ăcole Norm. Sup. (4) 39 (2006), no. 5, 775â839 (English, with English and French summaries). MR 2292633, DOI 10.1016/j.ansens.2006.08.001
- Matthew Emerton, On the interpolation of systems of eigenvalues attached to automorphic Hecke eigenforms, Invent. Math. 164 (2006), no. 1, 1â84. MR 2207783, DOI 10.1007/s00222-005-0448-x
- M. Emerton, Jacquet modules of locally analytic representations of $p$-adic reductive groups II. The relation to parabolic induction, to appear in J. Inst. Math. Jussieu.
- C. T. Féaux de Lacroix. $p$-adische Distributionen, Diplomarbeit, Köln, 1992.
- Christian Tobias FĂ©aux de Lacroix, Einige Resultate ĂŒber die topologischen Darstellungen $p$-adischer Liegruppen auf unendlich dimensionalen VektorrĂ€umen ĂŒber einem $p$-adischen Körper, Schriftenreihe des Mathematischen Instituts der UniversitĂ€t MĂŒnster. 3. Serie, Heft 23, Schriftenreihe Math. Inst. Univ. MĂŒnster 3. Ser., vol. 23, Univ. MĂŒnster, Math. Inst., MĂŒnster, 1999, pp. x+111 (German). MR 1691735
- A. W. Ingleton, The Hahn-Banach theorem for non-Archimedean valued fields, Proc. Cambridge Philos. Soc. 48 (1952), 41â45. MR 45939
- Nathan Jacobson, Abstract derivation and Lie algebras, Trans. Amer. Math. Soc. 42 (1937), no. 2, 206â224. MR 1501922, DOI 10.1090/S0002-9947-1937-1501922-7
- Reinhardt Kiehl, Theorem A und Theorem B in der nichtarchimedischen Funktionentheorie, Invent. Math. 2 (1967), 256â273 (German). MR 210949, DOI 10.1007/BF01425404
- Michel Lazard, Groupes analytiques $p$-adiques, Inst. Hautes Ătudes Sci. Publ. Math. 26 (1965), 389â603 (French). MR 209286
- Yasuo Morita, Analytic representations of $\textrm {SL}_2$ over a ${\mathfrak {p}}$-adic number field. III, Automorphic forms and number theory (Sendai, 1983) Adv. Stud. Pure Math., vol. 7, North-Holland, Amsterdam, 1985, pp. 185â222. MR 876106, DOI 10.2969/aspm/00710185
- P. Schneider, J. Teitelbaum, and Dipendra Prasad, $U({\mathfrak {g}})$-finite locally analytic representations, Represent. Theory 5 (2001), 111â128. With an appendix by Dipendra Prasad. MR 1835001, DOI 10.1090/S1088-4165-01-00109-1
- A. P. Robertson and W. J. Robertson, Topological vector spaces, Cambridge Tracts in Mathematics and Mathematical Physics, No. 53, Cambridge University Press, New York, 1964. MR 0162118
- Peter Schneider, Nonarchimedean functional analysis, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2002. MR 1869547
- P. Schneider, $p$-adische analysis, Vorlesung in MĂŒnster, 2000; available electronically at http://www.math.uni-muenster.de/math/u/schneider/publ/lectnotes
- Peter Schneider and Jeremy Teitelbaum, $p$-adic boundary values, AstĂ©risque 278 (2002), 51â125. Cohomologies $p$-adiques et applications arithmĂ©tiques, I. MR 1922824
- Peter Schneider and Jeremy Teitelbaum, Locally analytic distributions and $p$-adic representation theory, with applications to $\textrm {GL}_2$, J. Amer. Math. Soc. 15 (2002), no. 2, 443â468. MR 1887640, DOI 10.1090/S0894-0347-01-00377-0
- P. Schneider, J. Teitelbaum, and Dipendra Prasad, $U({\mathfrak {g}})$-finite locally analytic representations, Represent. Theory 5 (2001), 111â128. With an appendix by Dipendra Prasad. MR 1835001, DOI 10.1090/S1088-4165-01-00109-1
- P. Schneider and J. Teitelbaum, Banach space representations and Iwasawa theory, Israel J. Math. 127 (2002), 359â380. MR 1900706, DOI 10.1007/BF02784538
- P. Schneider and J. Teitelbaum, $p$-adic Fourier theory, Doc. Math. 6 (2001), 447â481. MR 1871671
- Peter Schneider and Jeremy Teitelbaum, Algebras of $p$-adic distributions and admissible representations, Invent. Math. 153 (2003), no. 1, 145â196. MR 1990669, DOI 10.1007/s00222-002-0284-1
- Jean-Pierre Serre, Lie algebras and Lie groups, W. A. Benjamin, Inc., New York-Amsterdam, 1965. Lectures given at Harvard University, 1964. MR 0218496