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