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 theory to mathematical physics and geometry.

"This book is dedicated to the memory of Issai Schur, one of the brilliant stars in mathematical heaven and an unsurpassed teacher. It is divided into two parts. In the first one among others reminiscences from students and members of Schurs family are presented, followed by a biographical sketch through letters and other documents and an extensive review of his lesser known contributions to analysis. The second part contains 13 contributions to representation theory. Schur proper field of research. . . Many of these articles are inspired by Schurs work showing how fertile his ideas are even [for] today."

---Monatshefte für Mathematik

Klappentext
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. TOC:H. H. Andersen, N. Lauritzen "Twisted Verma Modules" A. Braverman,D. Kazhdan "Gamma-Sheaves on Reductive Groups" S. Donkin"Representations of Hecke Algebras and Characters of Symmetric Groups" B. Kostant "Dirac Cohomology for the Cubic Dirac Operator" A.Lascoux "Double Crystal Graphs" B. Leclerc, M. Nazarov, J.-Y. Thibon"Induced Representations of Affine Hecke Algebras and Canonical Basesof Quantum Groups" P.Littelmann, C.S. Seshadri "A Pieri-ChevalleyFormula for K(G/B) and Standard Monomial Theory" G. Luzstig"Constructible Functions on Varieties Attached to Quivers" O.Mathieu "On the Endomorphism Algebra of the Steinberg Module" G.Olshanski, A. Regev, A. Vershik "Schur-Frobenius Functions" E. Opdam"A Generating Function for the Trace of the Iwahori-Hecke Algebra" M. Reineke "Quivers, Desingularizations and Canonical Bases" E.Vasserot, M Varagnolo "Perverse Sheaves and Quantum GrothendieckRings"

Inhalt
Twisted Verma Modules.- ?-Sheaves on Reductive Groups.- Representations of Hecke Algebras and Characters of Symmetric Groups.- Dirac Cohomology for the Cubic Dirac Operator.- Double Crystal Graphs.- Induced Representations of Affine Hecke Algebras and Canonical Bases of Quantum Groups.- A Pieri-Chevalley Type Formula for K(G/B) and Standard Monomial Theory.- Constructible Functions on Varieties Attached to Quivers.- On the Endomorphism Algebra of the Steinberg Module.- Frobenius-Schur Functions.- A Generating Function for the Trace of the Iwahori-Hecke Algebra.- Quivers, Desingularizations and Canonical Bases.- Perverse Sheaves and Quantum Grothendieck Rings.