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Vilenkin N.Ja., Klimyk A.U. — Representation of Lie groups and special functions. Recent advances
Vilenkin N.Ja., Klimyk A.U. — Representation of Lie groups and special functions. Recent advances

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Название: Representation of Lie groups and special functions. Recent advances

Авторы: Vilenkin N.Ja., Klimyk A.U.

Аннотация:

The present book is a continuation of the three-volume work Representation of Lie Groups and Special Functions by the same authors. Here, they deal with the exposition of the main new developments in the contemporary theory of multivariate special functions, bringing together material that has not been presented in monograph form before. The theory of orthogonal symmetric polynomials (Jack polynomials, Macdonald's polynomials and others) and multivariate hypergeometric functions associated to symmetric polynomials are treated. Multivariate hypergeometric functions, multivariate Jacobi polynomials and h-harmonic polynomials connected with root systems and Coxeter groups are introduced. Also, the theory of Gel'fand hypergeometric functions and the theory of multivariate hypergeometric series associated to Clebsch — Gordan coefficients of the unitary group U(n) is given. The volume concludes with an extensive bibliography. For research mathematicians and physicists, postgraduate students in mathematics and mathematical and theoretical physics.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1994

Количество страниц: 511

Добавлена в каталог: 29.01.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Annihilation operator      333
Appell function, $F_{1}$      209
Appell function, $F_{2}$      209
Appell function, $F_{3}$      209
Appell function, $F_{4}$      210
b-function      396
Biedenharn — Elliott identity      316
Boson polynomial      340
Boson polynomial, dual      340
Cartan subalgebra      265
Cartan subgroup      265
Cartan — Weyl basis      267
Clebsch — Gordan coefficient      290
Configuration      444
Coxeter graph      6
Coxeter group      4
Coxeter group, irreducible      5
Coxeter matrix      6
Coxeter number      8
Creation operator      333
Crystalographic group      7
Defining relations      2
Degree of submanifold      406
Denominator function      326
Denominator function, elementary      331
Dihendral group      1
Dominance ordering      69
Gauss decomposition      269
Generalized binomial coefficient      127
Generalized Hankel transform      221
Generalized Laplace transform      213
Grassmannian complex      428
Grassmannian real      419
Green polynomial      102
Group algebra      15
h-Bessel function      64
h-Hankel transform      61
h-Laplacian      19
Hall — Littlewood function      94
Hall — Littlewood polynomial      94
Hall — Littlewood polynomial, skew      103
Harish-Chandra c-function      226
Horizontal m-strip      69
Horn hypergeometric series      395
Horn hypergeometric system      397
Horn q-hypergeometric series      412
Hypergeometric function general      405
Hypergeometric function on Grassmannian      423
Hypergeometric function on stratum      442
Hypergeometric series general      398
Hypergeometric system general      405
Hypergeometric system on Grassmannian      425
Idempotent primitive      15
Iwasawa decomposition      269
Jack polynomial      107
Jack polynomial, skew      117
Jack symmetric function      107
Kostka number      85
LADDER      430
Lattice permutation      83
Lenght of element      5
Lenght of partition      67
Littlewood — Richardson rule      83
M-subspace      439
Macdonald symmetric function      150
Macdonald symmetric polynomial      149
Matrix lower triangular      83
Matrix lower unitriangular      83
Matrix upper triangular      83
Matrix upper unitriangular      83
Minimum principle      32
Multiplicity of representation      276
Multiplicity of weight      270
Multiplicity problem      322
One-orbit stratum      443
Operator avaraging      30
Operator intertwining      47
Operator projective      325
Part of partition      67
Partition      67
Path sum formula      330
Pattern calculus rules      327
Pieri's rule      89
Pluecker coordinates      421
Poisson kernel      58
Polynomial h-harmonic      21
q-Hypergeometric series general      414
Racah coefficient      311
Radon transform      421
Reduction relation      438
Regular element      265
Representation analytical      269
Representation complex      269
Representation fundamental      272
Representation real-analytical      269
Reverse lexicographic order      68
Root      7 154
Root subspace      266
Root system      7 154
Root system, irreducible      155
Root system, reduced      155
Root, indivisible      155
Root, negative      155
Root, positive      155
Root, simple      155 268
Scalar factor      303
Schur function      77
Schur function, skew      86
Schur polynomial      77
Skew shape      69
Stratum      442
Stratum, general      442
Stratum, nondegeneral      443
Stratum, p-parametric      443
Stretched Wigner operator      326
Subgroup chain      300
Symmetric function complete      73
Symmetric function elementary      72
Symmetric function, power-sum      74
Symmetric polynomial complete      73
Symmetric polynomial elementary      73
Symmetric polynomial monomial      70
Tableau      69
Tableau, standard      69
Tricomi theorem      222
Vacuum state vector      334
Vertical m-strip      69
wall      268
Weight      156
Weight of partition      67
Weight of tableau      69
Weight of word      99
Weight, dominant      156 271
Weight, fundamental      156
Weight, highest      271
Weight, integral      271
Weight, subspace      270
Weight, vector      270
Weyl chamber      155
Weyl group      154 267
Word      83
Word, standard      99
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