Index
absolutely semisimple, 136
Arthur’s trace formula, 5
Arthur, James, 5
atomic measure, 49
automorphic
representation, 3
automorphic induction, 63
autormophic induction, 32
bad places, 72
base change, 9, 71, 72, 95, 102, 131–133
conjugacy, 22
F -conjugacy, 22
¯-conjugacy,
F see also conjugacy, stable
stable, 22
conjugacy class
elliptic, 6
regular, 6
continuous spectrum, 4
contribution
exclusive, 73
convolution operator, 4, 6, 30, 32, 85
discrete spectrum, 4
discriminant, 142
dual group, 18, 20
element
elliptic, 22, 137–141
G-regular, 23
parabolic, 41
regular, 22
semisimple, 22
singular, 22
type, 26
elliptic, see also element, elliptic
elliptic component, see also elliptic
function, see also representation,
elliptic
elliptic function, 48
endoscopic
data, 15–21
equivalent, 16
group, 6, 7, 15–21, 42, 85
endoscopic group, 96
ε-character, see also Harish-Chandra
character, 7
ε-endoscopic group, see also endoscopic,
group
ε-trace identity, 53
F-H class, see also Frobenius-Hecke class
fine χ-expansion, see also trace formula,
spectral side, 29–40
Frobenius-Hecke class, 7, 47, 54–59
function
elliptic, 26
regular, 8
type, 27
Fundamental Lemma, 28, 135
Galois action, 16
global datum, 47–48
H1, 96
H2, 96
Haar measure, 6, 85
Harish-Chandra, 70
Harish-Chandra character, 71
twisted, 71, 89
Hecke algebra, 4, 28, 135
Heisenberg parabolic subgroup, see also
parabolic subgroup, Heisenberg
Howe, Piatetski-Shapiro, 9
intertwining operator, 5, 30, 38, 70, 86, 88
Iwasawa decomposition, 89
Kazhdan decomposition, 136
Kottwitz-Shelstad’s trace formula, 6, 42–45
L-
action, 15
embedding, 17, 19, 22, 28
group, 7, 15
homomorphism, 15
Langlands correspondence, 16
Langlands quotient, 61
lattice, 23
171
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