**CBMS Regional Conference Series in Mathematics**

Volume: 42;
1980;
59 pp;
Softcover

MSC: Primary 22;
Secondary 33

Print ISBN: 978-0-8218-1692-9

Product Code: CBMS/42

List Price: $19.00

Individual Price: $15.20

**Electronic ISBN: 978-1-4704-2402-2
Product Code: CBMS/42.E**

List Price: $19.00

Individual Price: $15.20

# Special Functions and Linear Representations of Lie Groups

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*Jean Dieudonné*

A co-publication of the AMS and CBMS

#### Table of Contents

# Table of Contents

## Special Functions and Linear Representations of Lie Groups

- Cover Cover11 free
- Title i2 free
- Copyright ii3 free
- Contents iii4 free
- 1. Introduction 16 free
- 2. Representations of SU(2) 49 free
- 3. The general theory of linear representations of compact groups 914
- 4. Lie theory of representations of compact connected Lie groups 1520
- 5. Induced representations of compact groups 1722
- 6. Spherical functions on compact groups 1823
- 7. Examples; spherical harmonics 2126
- 8. The general theory of spherical functions 2530
- 9. Fourier and Plancherel transforms 3035
- 10. Extension of the Plancherel transform 3439
- 11. The subtleties of harmonic analysis 3742
- 12. Differential properties of spherical functions on Lie groups 4045
- 13. Spherical functions on semisimple Lie groups 4247
- 14. More on SL(2, R) 4550
- 15. Automorphic functions 5358
- 16. Groups of isometries and Bessel functions 5560
- 17. Other special functions 5863
- References 5964
- Back Cover Back Cover165

#### Reviews

Presented in a clear, self-contained, and well-organized way, these introductory level lectures are highly recommended for individual or in-class use for acquiring basic knowledge of the groups \({\mathbf SU}(2)\), \({\mathbf SO}(3)\), \({\mathbf SL}(2, \mathbf R)\), and their function theories. Covering representations of \({\mathbf SU}(2)\), spherical harmonics on \(S_n\), representations of the group \({\mathbf SL}(2, \mathbf R)\) and spherical functions with respect to its maximal compact subgroup \({\mathbf SO}(2)\), these lectures also take account of some well known functions exhibited as spherical or matrix-entry functions of unitary representations—for example, Jacobi polynomials and Legendre functions appear in this way for \({\mathbf SU}(2)\).

-- C. F. Dunkl, Mathematical Reviews