Lie Theory and Special Functions
Published on 14. May 2014
357 pages
978-0-08-095551-3 (ISBN)
Description
Lie Theory and Special Functions
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Series
Language
English
Place of publication
San Diego
United States
ISBN-13
978-0-08-095551-3 (9780080955513)
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Willard Miller
Lie Theory and Special Functions
Book
06/1968
Academic Press
€69.33
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Content
- 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
