Ebook: Studies in Memory of Issai Schur

This volume Studies in Memory of Issai Schur was conceived as a tribute to Schur's of his tragic end. His impact on great contributions to mathematics and in remembrance of mathematicians Representation Theory alone was so great that a significant number of Researchers (TMR) Network, in the European Community Training and Mobility Orbits, Crystals and Representation Theory, in operation during the period (1997-2002) have been occupied with what has been called Schur theory. Consequently, this volume has the additional purpose of recording some of the significant results of the network. It was furthermore appropriate that invited contributors should be amongst the speakers at the Paris Midterm Workshop of the network held at Chevaleret during 21-25 May, 2000 as well as those of the Schur Memoriam Workshop held at the Weizmann Institute, Rehovot, during 27-31 December 2000. The latter marked the sixtieth anniversary of Schur's passing and took place in the 125th year of his birth.

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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.

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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.
Content:
Front Matter....Pages i-clxxxviii
Twisted Verma Modules....Pages 1-26
?-Sheaves on Reductive Groups....Pages 27-47
Representations of Hecke Algebras and Characters of Symmetric Groups....Pages 49-67
Dirac Cohomology for the Cubic Dirac Operator....Pages 69-93
Double Crystal Graphs....Pages 95-114
Induced Representations of Affine Hecke Algebras and Canonical Bases of Quantum Groups....Pages 115-153
A Pieri-Chevalley Type Formula for K (G/B) and Standard Monomial Theory....Pages 155-176
Constructible Functions on Varieties Attached to Quivers....Pages 177-223
On the Endomorphism Algebra of the Steinberg Module....Pages 225-250
Frobenius-Schur Functions....Pages 251-299
A Generating Function for the Trace of the Iwahori-Hecke Algebra....Pages 301-323
Quivers, Desingularizations and Canonical Bases....Pages 325-344
Perverse Sheaves and Quantum Grothedieck Rings....Pages 345-365
Back Matter....Pages 367-369

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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.
Content:
Front Matter....Pages i-clxxxviii
Twisted Verma Modules....Pages 1-26
?-Sheaves on Reductive Groups....Pages 27-47
Representations of Hecke Algebras and Characters of Symmetric Groups....Pages 49-67
Dirac Cohomology for the Cubic Dirac Operator....Pages 69-93
Double Crystal Graphs....Pages 95-114
Induced Representations of Affine Hecke Algebras and Canonical Bases of Quantum Groups....Pages 115-153
A Pieri-Chevalley Type Formula for K (G/B) and Standard Monomial Theory....Pages 155-176
Constructible Functions on Varieties Attached to Quivers....Pages 177-223
On the Endomorphism Algebra of the Steinberg Module....Pages 225-250
Frobenius-Schur Functions....Pages 251-299
A Generating Function for the Trace of the Iwahori-Hecke Algebra....Pages 301-323
Quivers, Desingularizations and Canonical Bases....Pages 325-344
Perverse Sheaves and Quantum Grothedieck Rings....Pages 345-365
Back Matter....Pages 367-369
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