Lie Theory and Special Functions

Name: Lie Theory and Special Functions
Brand: Academic Press
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Miller(Herausgeber*in)

Academic Press

Erschienen am 14. Mai 2014

357 Seiten

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Front Cover
Lie Theory and Special Functions
Copyright Page
Contents
Preface
Chapter 1. Résumé of Lie Theory
1-1 Local Lie Groups
1-2 Examples
1-3 Local Transformation Groups
1-4 Examples of Local Transformation Groups
Chapter 2. Representations and Realizations of Lie Algebras
2-1 Representations of Lie Algebras
2-2 Realizations of Representations
2-3 Representations of L(O3)
2-4 The Angular Momentum Operators
2-5 The Lie Algebras G(a, b)
2-6 Representations of G(a, b)
2-7 Realizations of G(a, b) in Two Variables
2-8 Realizations of G(a, b) in One Variable
Chapter 3. Lie Theory and Bessel Functions
3-1 The Representations Q(?, mo)
3-2 Recursion Relations for the Matrix Elements
3-3 Realizations of Q(?, mo) in Two Variables
3-4 Weisner's Method for Bessel Functions
3-5 The Real Euclidean Group E3
3-6 Unitary Representations of Lie Groups
3-7 Induced Representations of E3
3-8 The Unitary Representations (p) of E3
3-9 The Matrix Elements of (p)
3-10 The Infinitesimal Operators of (p)
Chapter 4. Lie Theory und Confluent Hypergeometric Functions
4-1 The Representation R(?, mo, µ)
4-2 The Representation to ?,µ
4-3 The Representation
4-4 Differential Equations for the Matrix Elements
4-5 The Representation
4-6 A Realization of R(?, mo, µ ) by Type D Operators
4-7 A Realization of ?,µ by Type D' Operators
4-8 Transformations of Type C' Operators
4-9 Type C' Realizations of R(?, m0, µ)
4-10 Type C' Realizations of o,1
4-11 The Group S4
4-12 Induced Representations of G4
4-13 The Hilbert Space F
4-14 The Unitary Representation (?, I)
4-15 The Matrix Elements of (?, I)
4-16 The Unitary Representations (?,-I)
4-17 The Tensor Products (?, I) Q (?', l')
4-18 The Representations (?, I) Q (?', 4')
4-19 The Representations (?, I) Q (?', 4)
4-20 The Representations (p) Q (?, I)
4-21 A Contraction of G(0,1)
Chapter 5. Lie Theory and Hypergeometric Functions
5-1 The Representation Dµ( u, m0)
5-2 The Representation u
5-3 The Representation u
5-4 The Representation D(2u)
5-5 The Tensor Product D(2u) D(2u)
5-6 The Tensor Product u Q u
5-7 Differential Relations for the Matrix Elements
5-8 Type B Realizations of D(u, m0)
5-9 Type B Realizations of u
5-10 Weisner's Method for Type B Operators
5-11 Type A Realizations of D(u, m0)
5-12 Type A Realizations of u
5-13 Type A Realizations of u
5-14 Type A Realizations of D(2u)
5-15 Weisner's Method for Type A Operators
5-16 The Group SU(2)
5-17 The Group G3
5-18 Unitary Representations of G3
5-19 Contractions of g(1, 0)
Chapter 6. Special Functions Related to the Euclidean Group in 3-Space
6-1 Representations of g6
6-2 Type E Operators
6-3 Type F Operators
6-4 The Euclidean Group E6
6-5 The Matrix Elements of (?, s)
Chapter 7. The Factorization Method
7-1 Recurrence Relations
7-2 The Factorization Types
Chapter 8. Generulized Lie Derivatives
8-1 Generalized Derivations
8-2 Cohomology Classes of Realizations
8-3 Computation of the Cohomology Classes
8-4 Tables of Cohomology Classes
Chapter 9. Some Generulizutions
9-1 The Lie Algebra K5
9-2 The Lie Group K5
9-3 Representations of K5
9-4 The Representation R'(?, m0, µ)
9-5 The Representation ', ?µ
9-6 The Lie Algebra gp,q
9-7 The Lie Group Gp,q
9-8 Representations of gp,q
9-9 Recursion Relations for the Matrix Elements
9-10 Realizations in Two Variables
9-11 Generating Functions for Generalized Bessel Functions
Appendix
1 The Gamma Function
2 The Hypergeometric Function
3 The Confluent Hypergeometric Function
4 Parabolic Cylinder Functions
5 Bessel Functions
Bibliography
Index

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