Paper XI: Packets, Arithmetic Realization, and Conditional Comparison

Download original file

This is the original source text. Reading it does not run or verify the program.

Read the typeset paper

1 \providecommand{\bysame}{\leavevmode\hbox to3em{\hrulefill}\thinspace}
2 \providecommand{\MR}{\relax\ifhmode\unskip\space\fi MR }
3 % \MRhref is called by the amsart/book/proc definition of \MR.
4 \providecommand{\MRhref}[2]{%
5   \href{http://www.ams.org/mathscinet-getitem?mr=#1}{#2}
6 }
7 \providecommand{\href}[2]{#2}
8 \begin{thebibliography}{10}
9 
10 \bibitem{BerndtEvansWilliams1998}
11 Bruce~C. Berndt, Ronald~J. Evans, and Kenneth~S. Williams, \emph{{Gauss} and
12   {Jacobi} sums}, Canadian Mathematical Society Series of Monographs and
13   Advanced Texts, Wiley, New York, 1998.
14 
15 \bibitem{Blondel2012}
16 Corinne Blondel, \emph{Repr\'esentation de {Weil} et beta extensions}, Annales
17   de l'Institut Fourier \textbf{62} (2012), no.~4, 1319--1366.
18 
19 \bibitem{Brown1982}
20 Kenneth~S. Brown, \emph{Cohomology of groups}, Graduate Texts in Mathematics,
21   vol.~87, Springer, New York, 1982.
22 
23 \bibitem{BushnellHenniart1996}
24 Colin~J. Bushnell and Guy Henniart, \emph{Local tame lifting for {GL(N)}. {I}.
25   simple characters}, Publications Math\'ematiques de l'IH\'ES \textbf{83}
26   (1996), 105--233.
27 
28 \bibitem{BushnellHenniart1999}
29 \bysame, \emph{Local tame lifting for {GL(N)}. {II}. wildly ramified
30   supercuspidals}, Ast\'erisque, vol. 254, Soci\'et\'e Math\'ematique de
31   France, 1999.
32 
33 \bibitem{BushnellHenniart2005ET1}
34 \bysame, \emph{The essentially tame local {Langlands} correspondence. {I}},
35   Journal of the American Mathematical Society \textbf{18} (2005), no.~3,
36   685--710.
37 
38 \bibitem{BushnellHenniart2005ET2}
39 \bysame, \emph{The essentially tame local {Langlands} correspondence. {II}.
40   totally ramified representations}, Compositio Mathematica \textbf{141}
41   (2005), no.~4, 979--1011.
42 
43 \bibitem{BushnellHenniart2006}
44 \bysame, \emph{The local {Langlands} conjecture for {GL(2)}}, Grundlehren der
45   mathematischen Wissenschaften, vol. 335, Springer, Berlin, 2006.
46 
47 \bibitem{BushnellHenniart2010ET3}
48 \bysame, \emph{The essentially tame local {Langlands} correspondence. {III}.
49   the general case}, Proceedings of the London Mathematical Society
50   \textbf{101} (2010), no.~2, 497--553.
51 
52 \bibitem{BushnellHenniart2017}
53 \bysame, \emph{Higher ramification and the local {Langlands} correspondence},
54   Annals of Mathematics \textbf{185} (2017), no.~3, 919--955.
55 
56 \bibitem{BushnellKutzko1993}
57 Colin~J. Bushnell and Philip~C. Kutzko, \emph{The admissible dual of {GL(N)}
58   via compact open subgroups}, Annals of Mathematics Studies, vol. 129,
59   Princeton University Press, Princeton, 1993.
60 
61 \bibitem{DavenportHasse1935}
62 Harold Davenport and Helmut Hasse, \emph{Die nullstellen der
63   kongruenzzetafunktionen in gewissen zyklischen f\"allen}, Journal f\"ur die
64   reine und angewandte Mathematik \textbf{172} (1935), 151--182.
65 
66 \bibitem{DeligneLusztig1976}
67 Pierre Deligne and George Lusztig, \emph{Representations of reductive groups
68   over finite fields}, Annals of Mathematics \textbf{103} (1976), no.~1,
69   103--161.
70 
71 \bibitem{Dotto2022}
72 Andrea Dotto, \emph{Canonical beta extensions}, Documenta Mathematica
73   \textbf{27} (2022), 295--313.
74 
75 \bibitem{Gerardin1977}
76 Paul G\'erardin, \emph{{Weil} representations associated to finite fields},
77   Journal of Algebra \textbf{46} (1977), no.~1, 54--101.
78 
79 \bibitem{GurevichHadani2007}
80 Shamgar Gurevich and Ronny Hadani, \emph{The geometric {Weil} representation},
81   Selecta Mathematica. New Series \textbf{13} (2007), no.~3, 465--481.
82 
83 \bibitem{HarrisTaylor2001}
84 Michael Harris and Richard Taylor, \emph{The geometry and cohomology of some
85   simple {Shimura} varieties}, Annals of Mathematics Studies, vol. 151,
86   Princeton University Press, Princeton, 2001.
87 
88 \bibitem{Henniart1993}
89 Guy Henniart, \emph{Caract\'erisation de la correspondance de {Langlands}
90   locale par les facteurs {$\varepsilon$} de paires}, Inventiones Mathematicae
91   \textbf{113} (1993), no.~2, 339--350.
92 
93 \bibitem{Henniart2000}
94 \bysame, \emph{Une preuve simple des conjectures de {L}anglands pour {GL}(n)
95   sur un corps p adique}, Inventiones Mathematicae \textbf{139} (2000), no.~2,
96   439--455.
97 
98 \bibitem{HenniartLemaire2011}
99 Guy Henniart and Bertrand Lemaire, \emph{Changement de base et induction
100   automorphe pour {$\mathrm{GL}_n$} en caract{\'e}ristique non nulle},
101   M{\'e}moires de la Soci{\'e}t{\'e} Math{\'e}matique de France, no. 124,
102   Soci{\'e}t{\'e} math{\'e}matique de France, 2011.
103 
104 \bibitem{Isaacs1976}
105 I.~Martin Isaacs, \emph{Character theory of finite groups}, Academic Press, New
106   York, 1976.
107 
108 \bibitem{Karpilovsky1985}
109 Gregory Karpilovsky, \emph{Projective representations of finite groups},
110   Monographs and Textbooks in Pure and Applied Mathematics, vol.~94, Marcel
111   Dekker, New York, 1985.
112 
113 \bibitem{Mackey1952}
114 George~W. Mackey, \emph{Induced representations of locally compact groups.
115   {I}}, Annals of Mathematics \textbf{55} (1952), no.~1, 101--139.
116 
117 \bibitem{MilnorHusemoller1973}
118 John Milnor and Dale Husemoller, \emph{Symmetric bilinear forms}, Ergebnisse
119   der Mathematik und ihrer Grenzgebiete, vol.~73, Springer, Berlin, 1973.
120 
121 \bibitem{Neuhauser2002}
122 Markus Neuhauser, \emph{An explicit construction of the metaplectic
123   representation over a finite field}, Journal of Lie Theory \textbf{12}
124   (2002), no.~1, 15--30.
125 
126 \bibitem{Prasad2009}
127 Amritanshu Prasad, \emph{On character values and decomposition of the {Weil}
128   representation associated to a finite abelian group}, The Journal of Analysis
129   \textbf{17} (2009), 73--85.
130 
131 \bibitem{Serre1967}
132 Jean-Pierre Serre, \emph{Local class field theory}, Algebraic Number Theory
133   (J.~W.~S. Cassels and A.~Fr\"ohlich, eds.), Academic Press, London, 1967,
134   pp.~128--161.
135 
136 \bibitem{Serre1977}
137 \bysame, \emph{Linear representations of finite groups}, Graduate Texts in
138   Mathematics, vol.~42, Springer, New York, 1977.
139 
140 \bibitem{Tate1979}
141 John Tate, \emph{Number theoretic background}, Automorphic Forms,
142   Representations and {L}-Functions, Part 2 (Armand Borel and William
143   Casselman, eds.), Proceedings of Symposia in Pure Mathematics, vol.~33,
144   American Mathematical Society, 1979, pp.~3--26.
145 
146 \end{thebibliography}

Back to source controls

Back to Paper XI: Packets, Arithmetic Realization, and Conditional Comparison