Description:
The representation theory of the symmetric group, of Chevalley groups particularly in positive characteristic and of Lie algebraic systems, has undergone some remarkable developments in recent years. Many techniques are inspired by the great works of Issai Schur who passed away some 60 years ago. This volume is dedicated to his memory. This is a unified presentation consisting of an extended biography of Schur---written in collaboration with some of his former students---as well as survey articles on Schur's legacy (Schur theory, functions, etc). Additionally, there are articles covering the areas of orbits, crystals and representation theory, with special emphasis on canonical bases and their crystal limits, and on the geometric approach linking orbits to representations and Hecke algebra techniques. Extensions of representation theory to mathematical physics and geometry will also be presented. Contributors: Biography: W. Ledermann, B. Neumann, P.M. Neumann, H. Abelin- Schur; Review of work: H. Dym, V. Katznelson; Original papers: H. H. Andersen, A. Braverman, S. Donkin, V. Ivanov, D. Kazhdan, B. Kostant, A. Lascoux, N. Lauritzen, B. Leclerc, P. Littelmann, G. Luzstig, O. Mathieu, M. Nazarov, M. Reinek, J.-Y. Thibon, G. Olshanski, E. Opdam, A. Regev, C.S. Seshadri, M. Varagnolo, E. Vasserot, A. Vershik This volume will serve as a comprehensive reference as well as a good text for graduate seminars in representation theory, algebra, and mathematical physics