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