Studies in Memory of Issai Schur

1. Front Matter

   Pages i-clxxxviii

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2. Twisted Verma Modules

   • H. H. Andersen, N. Lauritzen

   Pages 1-26

3. γ-Sheaves on Reductive Groups

   • Alexander Braverman, David Kazhdan

   Pages 27-47

4. Representations of Hecke Algebras and Characters of Symmetric Groups

   • Stephen Donkin

   Pages 49-67

5. Dirac Cohomology for the Cubic Dirac Operator

   • Bertram Kostant

   Pages 69-93

6. Double Crystal Graphs

   • Alain Lascoux

   Pages 95-114

7. Induced Representations of Affine Hecke Algebras and Canonical Bases of Quantum Groups

   • Bernard Leclerc, Maxim Nazarov, Jean-Yves Thibon

   Pages 115-153

8. A Pieri-Chevalley Type Formula for K (G/B) and Standard Monomial Theory

   • P. Littelmann, C. S. Seshadri

   Pages 155-176

9. Constructible Functions on Varieties Attached to Quivers

   • G. Lusztig

   Pages 177-223

10. On the Endomorphism Algebra of the Steinberg Module

    • Olivier Mathieu

    Pages 225-250

11. Frobenius-Schur Functions

    • Grigori Olshanski, Amitai Regev, Anatoly Vershik, Vladimir Ivanov

    Pages 251-299

12. A Generating Function for the Trace of the Iwahori-Hecke Algebra

    • Eric M. Opdam

    Pages 301-323

13. Quivers, Desingularizations and Canonical Bases

    • Markus Reineke

    Pages 325-344

14. Perverse Sheaves and Quantum Grothedieck Rings

    • M. Varagnolo, E. Vasserot

    Pages 345-365

15. Back Matter

    Pages 367-369

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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.

• Cohomology
• Dirac
• Representation theory
• algebra
• homology
• math physics

"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

• Department of Mathematics, Weizmann Institute of Science, Rehovot, Israel

  Anthony Joseph

• Department of Mathematics, University of Haifa, Haifa, Israel

  Anna Melnikov

• Institut de Mathématiques, Univesité Pierre et Marie Curie, Paris Cedex, France

  Rudolf Rentschler

Policies and ethics