Index
© (Hilbert space direct sum), 5
-,
49
\A\ (A a linear map), 129
M A ,
86
MP,
52
, n , 20
ll(c d)llp, ll(c d)llA, 88
|[a]k (slash operator), 34
|r«r (slash operator), 34, 43
A, 68
A+, 68
Ak(N,u), 201
A, 55
A ^ (idelesof E), 311
A
5
, 55
a.e. (almost every), 55
A*, 57
A* , 57
A
1
, 87
Afin, 55
an(S), 16, 199
absolute value, 52
Ad(p), 153, 167
a d p O ( y ) = [X,Y], 152, 162
adeles, 55
adjoint, 131
of a function, 144
representation on 0c 153
admissible representation, 153
antiholomorphic discrete series, 190
archimedean, 52
arctan, 63
B (Borel subgroup), 3, 60
BG (Borel subsets of G), 70
BT, 252
B, 123
BT, 252
B(R) + , 14, 63
Banach space, 131
Beta function B(n,m), 289
Borel measure, 70
Borel subgroup, 60
Bruhat decomposition, 69
C(G) (cont. functions on G), 109
Co(X) (cont. functions vanishing at oo), 109
CC(G(A),UJ), 5
G
c
(G,x), 134
CC(X), 49
Cartan decomposition
p-adic, 208
real, 66, 68, 93
Cartan subalgebra, 162
Casimir element, 167
Cauchy-Schwarz inequality, 131
central character, 138
character value for 7Tk, 302
Chebyshev polynomial, 355
x(£iie2,si,S2)
(character of B(R)), 157
X7rk, 190
class group, 306
class number, 306
closed graph theorem, 131
closed linear transformation, 131
commensurable, 20
compact neighborhood, 49
complementary series, 186
conductor
of a character, 11, 196
of an order, 303
congruence subgroup, 8
conjugate-linear functional, 131
constant term, 4
countable additivity, 70
critical strip, 124
cusp
holomorphic at, 16
of T, 12
vanishing at, 17
cusp form, 18, 19
cuspidal function, 4
cuspidal representation, 5
D (subset of SL
2
(R)), 99
(subset of H), 19, 99
Do, 105, 261
373
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