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Special Functions and Linear Representations of Lie Groups
A co-publication of the AMS and CBMS.
 SEARCH THIS BOOK:
CBMS Regional Conference Series in Mathematics
1980; 59 pp; softcover
Number: 42
Reprint/Revision History:
reprinted 1982
ISBN-10: 0-8218-1692-6
ISBN-13: 978-0-8218-1692-9
List Price: US$18 Member Price: US$14.40
All Individuals: US\$14.40
Order Code: CBMS/42

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

• Introduction
• Representations of $$\mathbf {SU}(2)$$
• The general theory of linear representations of compact groups
• Lie theory of representations of compact connected Lie groups
• Induced representations of compact groups
• Spherical functions on compact groups
• Examples; spherical harmonics
• The general theory of spherical functions
• Fourier and Plancherel transforms
• Extension of the Plancherel transform
• The subtleties of harmonic analysis
• Differential properties of spherical functions on Lie groups
• Spherical functions on semisimple Lie groups
• More on $$\mathbf {SL}(2, \mathbf R)$$
• Automorphic functions
• Groups of isometries and Bessel functions
• Other special functions
• References