Algebraic Structures and Operators Calculus

Volume III: Representations of Lie Groups
1996. Auflage 1995
ISBN: 978-0-7923-3834-5
Verlag: Springer

Buch, Englisch, Band 347, 230 Seiten, Format (B × H): 160 mm x 240 mm, Gewicht: 589 g

Reihe: Mathematics and Its Applications

Introduction I. General remarks. 1 II. Notations. 5 III. Lie algebras: some basics. 8 Chapter 1 Operator calculus and Appell systems I. Boson calculus. 17 II. Holomorphic canonical calculus. 18 III. Canonical Appell systems. 23 Chapter 2 Representations of Lie groups I. Coordinates on Lie groups. 28 II. Dual representations. 29 III. Matrix elements. 37 IV. Induced representations and homogeneous spaces. 40 General Appell systems Chapter 3 I. Convolution and stochastic processes. 44 II. Stochastic processes on Lie groups. 46 III. Appell systems on Lie groups. 49 Chapter 4 Canonical systems in several variables I. Homogeneous spaces and Cartan decompositions. 54 II. Induced representation and coherent states. 62 III. Orthogonal polynomials in several variables. 68 Chapter 5 Algebras with discrete spectrum I. Calculus on groups: review of the theory. 83 II. Finite-difference algebra. 85 III. q-HW algebra and basic hypergeometric functions. 89 IV. su2 and Krawtchouk polynomials. 93 V. e2 and Lommel polynomials. 101 Chapter 6 Nilpotent and solvable algebras I. Heisenberg algebras. 113 II. Type-H Lie algebras. 118 Vll III. Upper-triangular matrices. 125 IV. Affine and Euclidean algebras. 127 Chapter 7 Hermitian symmetric spaces I. Basic structures. 131 II. Space of rectangular matrices. 133 III. Space of skew-symmetric matrices. 136 IV. Space of symmetric matrices. 143 Chapter 8 Properties of matrix elements I. Addition formulas. 147 II. Recurrences. 148 III. Quotient representations and summation formulas. 149 Chapter 9 Symbolic computations I. Computing the pi-matrices. 153 II. Adjoint group. 154 III. Recursive computation of matrix elements.

Zielgruppe

Research

Autoren/Hrsg.

Feinsilver, P.

Schott, René

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Mathematik | Informatik EDV | Informatik Informatik Logik, formale Sprachen, Automaten
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
• Mathematik | Informatik EDV | Informatik EDV & Informatik Allgemein
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis
• Mathematik | Informatik Mathematik Algebra Homologische Algebra

Inhaltsverzeichnis

I. General remarks.- II. Notations.- III. Lie algebras: some basics.- 1 Operator calculus and Appell systems.- I. Boson calculus.- II. Holomorphic canonical calculus.- III. Canonical Appell systems.- 2 Representations of Lie groups.- I. Coordinates on Lie groups.- II. Dual representations.- III. Matrix elements.- IV. Induced representations and homogeneous spaces.- 3 General Appell systems.- I. Convolution and stochastic processes.- II. Stochastic processes on Lie groups.- III. Appell systems on Lie groups.- 4 Canonical systems in several variables.- I. Homogeneous spaces and Cartan decompositions.- II. Induced representation and coherent states.- III. Orthogonal polynomials in several variables.- 5 Algebras with discrete spectrum.- I. Calculus on groups: review of the theory.- II. Finite-difference algebra.- III. q-HW algebra and basic hypergeometric functions.- IV. su2 and Krawtchouk polynomials.- V. e2 and Lommel polynomials.- 6 Nilpotent and solvable algebras.- I. Heisenberg algebras.- II. Type-H Lie algebras.- III. Upper-triangular matrices.- IV. Affine and Euclidean algebras.- 7 Hermitian symmetric spaces.- I. Basic structures.- II. Space of rectangular matrices.- III. Space of skew-symmetric matrices.- IV. Space of symmetric matrices.- 8 Properties of matrix elements.- I. Addition formulas.- II. Recurrences.- III. Quotient representations and summation formulas.- 9 Symbolic computations.- I. Computing the pi-matrices.- II. Adjoint group.- III. Recursive computation of matrix elements.- IV. Symbolic computation of Appell systems.- MAPLE output and procedures.- References.