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