"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 fur Mathematik

• 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.

"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 fur Mathematik

• 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.

"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 fur Mathematik

• 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.