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Advances in the Mathematical Sciences
Lie Groups and Symmetric Spaces: In Memory of F. I. Karpelevich
Edited by: S. G. Gindikin, Rutgers University, New Brunswick, NJ

American Mathematical Society Translations--Series 2
Advances in the Mathematical Sciences
2003; 355 pp; hardcover
Volume: 210
ISBN-10: 0-8218-3472-X
ISBN-13: 978-0-8218-3472-5
List Price: US$131
Member Price: US$104.80
Order Code: TRANS2/210
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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.


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

Table of Contents

  • D. N. Akhiezer -- Asymptotic distribution of eigenvalues for certain elements of the group ring of a compact Lie group
  • D. V. Alekseevsky and A. J. Di Scala -- Minimal homogeneous submanifolds of symmetric spaces
  • J.-P. Anker and P. Ostellari -- The heat kernel on noncompact symmetric spaces
  • E. M. Baruch, I. Piatetski-Shapiro, and S. Rallis -- On the uniqueness of Fourier Jacobi models for representations of \(U(2,1)\)
  • J. Bernstein and S. Gindikin -- Notes on integral geometry for manifolds of curves
  • B. Enriquez and P. Etingof -- Quantization of Alekseev-Meinrenken dynamical \(r\)-matrices
  • J. Faraut -- Analysis on the crown of a Riemannian symmetric space
  • I. Gelfand, V. Retakh, and R. L. Wilson -- Quaternionic quasideterminants and determinants
  • S. Gindikin -- Product formula for \(c\)-function and inverse horospherical transform
  • J. Hilgert, A. Pasquale, and E. B. Vinberg -- The dual horospherical Radon transform as a limit of spherical Radon transforms
  • A. W. Knapp -- The Gindikin-Karpelevič formula and intertwining operators
  • T. Kobayashi and S. Nasrin -- Multiplicity one theorem in the orbit method
  • B. Krötz and G. Ólafsson -- The c-function for non-compactly causal symmetric spaces and its relations to harmonic analysis and representation theory
  • I. G. Macdonald -- A formal identity for affine root systems
  • V. F. Molchanov -- Canonical representations and overgroups
  • Y. A. Neretin -- Pencils of geodesics in symmetric spaces, Karpelevich boundary, and associahedron-like polyhedra
  • M. A. Olshanetsky and V.-B. K. Rogov -- Poisson formula for a family of non-commutative Lobachevsky spaces
  • A. L. Onishchik -- Real semisimple Lie algebras and their representations
  • T. Oshima -- A calculation of \(c\)-functions for semisimple symmetric spaces
  • P. Sawyer -- The Abel transform on symmetric spaces of noncompact type
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