The Admissible Dual of GL(N) Via Compact Open Subgroups

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Princeton University Press, 1993 - Mathematics - 313 pages
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This work gives a full description of a method for analyzing the admissible complex representations of the general linear group G = Gl(N,F) of a non-Archimedean local field F in terms of the structure of these representations when they are restricted to certain compact open subgroups of G. The authors define a family of representations of these compact open subgroups, which they call simple types. The first example of a simple type, the "trivial type," is the trivial character of an Iwahori subgroup of G. The irreducible representations of G containing the trivial simple type are classified by the simple modules over a classical affine Hecke algebra. Via an isomorphism of Hecke algebras, this classification is transferred to the irreducible representations of G containing a given simple type. This leads to a complete classification of the irreduc-ible smooth representations of G, including an explicit description of the supercuspidal representations as induced representations. A special feature of this work is its virtually complete reliance on algebraic methods of a ring-theoretic kind. A full and accessible account of these methods is given here.

  

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Contents

III
19
V
24
VI
28
VII
35
VIII
43
IX
46
X
49
XII
51
XXXI
176
XXXII
177
XXXIII
181
XXXIV
195
XXXV
199
XXXVII
202
XXXVIII
207
XXXIX
208

XIII
57
XIV
65
XV
76
XVI
83
XVII
89
XIX
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XX
104
XXI
114
XXII
116
XXIII
126
XXIV
143
XXVI
146
XXVII
152
XXVIII
157
XXIX
158
XXX
165
XL
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XLI
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XLII
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XLIII
234
XLIV
241
XLV
256
XLVI
265
XLVII
266
XLVIII
275
XLIX
290
L
297
LI
298
LII
307
LIII
311
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Page x - Let P be a parabolic subgroup of G, with unipotent radical U, and suppose that P/U ^GL(NlF}x ...xGL(N,,F).
Page 11 - F = a non-Archimedean local field; OF = the discrete valuation ring in F; Pf = the maximal ideal of OF...

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