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Many techniques in representation theory and algebra have been inspired by the great works of Issai Schur who passed away some 60 years ago. This volume is dedicated to his memory. This unified presentation consists 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 25 articles covering a broad range of topics with extensions of representation. 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.
