Index
Appell’s hypergeometric function, 22, 24,
110, 119
associated Legendre function, 111, 113
associated variety, 13, 14
asymptotic behavior
—, σ−(fl,k), 66
—, Kl,k, 68
—, Γp,q
m,n
λ
a1,...,ap
b1,...,bq
, 91
—, fl,k, 56
—, Bessel distribution, 10
—, Bessel function, 109
—, G-function, 117
—, gamma function, 70
asymptotic support, 14
backward light cone, 11
Barnes generalized hypergeometric
function, 116
Bessel differential equation, 107
Bessel distribution, 10, 77, 98
—, differential equation, 102
—, integral expression, 93
—, Laurent series expansion, 12
Bessel function
—, of the first kind, 107
—, of the second kind, 107
bipolar coordinate, 23
boundary value, 19
Cartan involution, 34, 43
Cartan–Helgason theorem, 21
Cauchy’s principal value, 107
cohomological induction, 13
conformal compactification, 30
conformal inversion, 18, 43
conformal model, 2, 17, 28, 120
conserved quantity, 20
differentiable vector, 35
Dirac delta function, 31, 45, 106
discretely decomposable branching law, 21
distribution vector, 44
Euclidean Fourier transform, 5, 19, 22, 81
Euler operator, 4, 36
Euler vector field, 41
forward light cone, 11
Fourier–Hankel transform, 20
Fox’s reciprocal formula, 61
fundamental differential operator, 2, 4, 37,
102
Funk–Hecke formula, 82, 86, 122
Gauss’s duplication formula, 112
Gegenbauer polynomial, 24, 81, 111, 114
Gelfand triple, 44
Gelfand–Gindikin program, 19
Gelfand–Kirillov dimension, 13
generalized function, 46
geometric quantization, 14
Green function, 21
Hankel transform, 2, 23, 24, 61, 110, 120
Hankel’s notation, 110
harmonic representation, 15
Heisenberg Lie algebra, 9
Hermite semigroup, 19
highest weight module, 16, 19, 53, 60, 62
holomorphic semigroup, 19, 78
I-Bessel function, 108
indefinite orthogonal group, 16
indefinite orthogonal Lie algebra, 9
integral of Euler’s type, 120
intrinsic inner product, 20
isotropic cone, 4, 11
J-Bessel function, 108
Jordan algebra, 43
K-Bessel function, 22, 24, 108
K-picture, 17, 27
Kantor–Koecher–Tits group, 43
Knapp–Stein intertwining operator, 21
Kostant–Sekiguchi correspondence, 14
L2-model, 20, 120
ladder representation, 24
Laguerre semigroup, 19
131
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