**American Mathematical Society Translations - Series 2
Advances in the Mathematical Sciences**

2003; 355 pp; Hardcover

MSC: Primary 22; 53; 00;

Print ISBN: 978-0-8218-3472-5

Product Code: TRANS2/210

Print ISBN: 978-0-8218-3472-5

Product Code: TRANS2/210

List Price: $131.00

Individual Member Price: $104.80

**Electronic ISBN: 978-1-4704-3421-2
Product Code: TRANS2/210.E**

List Price: $131.00

Individual Member Price: $104.80

# Lie Groups and Symmetric Spaces: In Memory of F. I. Karpelevich

Share this page *Edited by *
*S. G. Gindikin*

The book contains survey and research articles devoted mainly to
geometry and harmonic analysis of symmetric spaces and to corresponding aspects
of group representation theory. The volume is dedicated to the memory of
Russian mathematician, F. I. Karpelevich (1927–2000).

Of particular interest are the survey articles by Sawyer on the Abel
transform on noncompact Riemannian symmetric spaces, and by Anker and Ostellari
on estimates for heat kernels on such spaces, as well as the article by
Bernstein and Gindikin on integral geometry for families of curves.
There are also many research papers on topics of current interest.

The book is suitable for graduate students and research mathematicians
interested in harmonic analysis and representation theory.

#### Table of Contents

# Table of Contents

## Lie Groups and Symmetric Spaces: In Memory of F. I. Karpelevich

- Cover Cover11
- Frontispiece ii3
- Title page iii4
- Copyright page iv5
- Contents v6
- Preface vii8
- Friedrich Karpelevich: His early years in mathematics xi12
- Asymptotic distribution of eigenvalues for certain elements of the group ring of a compact Lie group 114
- Minimal homogeneous submanifolds of symmetric spaces 1124
- The heat kernel on noncompact symmetric spaces 2740
- On the uniqueness of Fourier Jacobi models for representations of 𝑈(2,1) 4760
- Notes on integral geometry for manifolds of curves 5770
- Quantization of Alekseev-Meinrenken dynamical 𝑟-matrices 8194
- Analysis on the crown of a Riemannian symmetric space 99112
- Quaternionic quasideterminants and determinants 111124
- Product formula for 𝑐-function and inverse horospherical transform 125138
- The dual horospherical Radon transform as a limit of spherical Radon transforms 135148
- The Gindikin-Karpelevič formula and intertwining operators 145158
- Multiplicity one theorem in the orbit method 161174
- The c-function for non-compactly causal symmetric spaces and its relations to harmonic analysis and representation theory 171184
- A formal identity for affine root systems 195208
- Canonical representations and overgroups 213226
- Pencils of geodesics in symmetric spaces, Karpelevich boundary, and associahedron-like polyhedra 225238
- Poisson formula for a family of non-commutative Lobachevsky spaces 257270
- Real semisimple Lie algebras and their representations 273286
- A calculation of 𝑐-functions for semisimple symmetric spaces 307320
- The Abel transform on symmetric spaces of noncompact type 331344
- Back Cover Back Cover1369

#### Readership

Graduate students and research mathematicians interested in harmonic analysis and representation theory.