Studies in Memory of Issai Schur

by Joseph, Anthony; Melnikov, Anna; Rentschler, Rudolf; Schur, Issai; Melnikov, Anna; Rentschler, Rudolf

• ISBN13: 9780817642082
• ISBN10: 0817642080
• Format: Hardcover
• Copyright: 2003-02-01
• Publisher: Birkhauser

Summary

This volume is dedicated to the memory of Issai Schur. It opens with some biographical reminiscences of the famous school he established in Berlin, his brutal dismissal by the Nazi regime and his tragic end in Palestine. This is followed by an extensive review of the extraordinary impact of his lesser known analytic work. Finally, leading mathematicians in the representation theory of the symmetric groups, of semisimple and affine Lie algebras and of Chevalley groups have contributed original and outstanding articles. These concern many areas inspired by Schur's work as well as more recent developments involving crystal and canonical bases, Hecke algebras, and the geometric approach linking orbits to representations.Contributors: Biography: H. Abelin-Schur, W. Ledermann, Y. Ne'eman,B. Neumann, P.M. Neumann, M. Sonis. Review: H. Dym, V. Katsnelson. 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, G. Olshanski, E. Opdam, A. Regev, M. Reineke, C.S. Seshadri, J.-Y. Thibon, M. Varagnolo, E. Vasserot, A. Vershik.The first part of this book will appeal to a general audience. The second part will be of interest to graduate students especially those in analysis, while the third part is addressed to specialists in Lie algebras.

Table of Contents

Preface	ix
In Memoriam - Issai Schur	xi
Anthony Joseph
Anna Melnikov
A Special Hour of Reminiscences	xix
Anthony Joseph
Issai Schur Died Here: Some Background Comments, In Memoriam	xxi
Yuval Ne'eman
Some Personal Recollections	xxxi
Bernhard Neumann
Some Personal Reminiscences of Issai Schur	xxxiii
Walter Ledermann
Schur's Influence on My Career	xxxvii
Walter Ledermann
A Story About Father	xli
Hilda Abelin-Schur
Issai Schur and his Library in Tel-Aviv	xliii
Michael Sonis
The Life of Issai Schur through Letters and other Documents	xlv
Walter Ledermann
Peter M. Neumann
Contributions of Issai Schur to Analysis	xci
Harry Dym
Victor Katsnelson
Twisted Verma Modules	1	(26)
H. H. Andersen
N. Lauritzen
γ-Sheaves on Reductive Groups	27	(22)
Alexander Braverman
David Kazhdan
Representations of Hecke Algebras and Characters of Symmetric Groups	49	(20)
Stephen Donkin
Dirac Cohomology for the Cubic Dirac Operator	69	(26)
Bertram Kostant
Double Crystal Graphs	95	(20)
Alain Lascoux
Induced Representations of Affine Hecke Algebras and Canonical Bases of Quantum Groups	115	(40)
Bernard Leclerc
Maxim Nazarov
Jean-Yves Thibon
A Pieri-Chevalley Type Formula for K (G/B) and Standard Monomial Theory	155	(22)
P. Littelmann
C.S. Seshadri
Constructible Functions on Varieties Attached to Quivers	177	(48)
G. Lusztig
On the Endomorphism Algebra of the Steinberg Module	225	(26)
Olivier Mathieu
Frobenius-Schur Functions	251	(50)
Grigori Olshanski
Amitai Regev
Anatoly Vershik
Vladimir Ivanov
A Generating Function for the Trace of the Iwahori-Hecke Algebra	301	(24)
Eric M. Opdam
Quivers, Desingularizations and Canonical Bases	325	(20)
Markus Reineke
Perverse Sheaves and Quantum Grothendieck Rings	345
M. Varagnolo
E. Vasserot