eBook ISBN:  9781470401764 
Product Code:  MEMO/124/591.E 
List Price:  $46.00 
MAA Member Price:  $41.40 
AMS Member Price:  $27.60 
eBook ISBN:  9781470401764 
Product Code:  MEMO/124/591.E 
List Price:  $46.00 
MAA Member Price:  $41.40 
AMS Member Price:  $27.60 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 124; 1996; 119 ppMSC: Primary 16; 20; 17;
Suppose that \(R\) is a finite dimensional algebra and \(T\) is a right \(R\)module. Let \(A = \mathrm{ End}_R(T)\) be the endomorphism algebra of \(T\). This memoir presents a systematic study of the relationships between the representation theories of \(R\) and \(A\), especially those involving actual or potential structures on \(A\) which ”stratify” its homological algebra. The original motivation comes from the theory of Schur algebras and the symmetric group, Lie theory, and the representation theory of finite dimensional algebras and finite groups.
The book synthesizes common features of many of the above areas, and presents a number of new directions. Included are an abstract ”Specht/Weyl module” correspondence, a new theory of stratified algebras, and a deformation theory for them. The approach reconceptualizes most of the modular representation theory of symmetric groups involving Specht modules and places that theory in a broader context. Finally, the authors formulate some conjectures involving the theory of stratified algebras and finite Coexeter groups, aiming toward understanding the modular representation theory of finite groups of Lie type in all characteristics.
ReadershipGraduate students and research mathematicians interested in representation theory of algebraic and finite groups, finitedimensional algebras, and Lie algebras.

Table of Contents

Chapters

Introduction

1. Preliminaries

2. Stratified algebras

3. Stratifying endomorphism algebras

4. Stratifications and orders in semisimple algebras

5. Examples

6. Some conjectures for finite Coxeter groups and further remarks


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Suppose that \(R\) is a finite dimensional algebra and \(T\) is a right \(R\)module. Let \(A = \mathrm{ End}_R(T)\) be the endomorphism algebra of \(T\). This memoir presents a systematic study of the relationships between the representation theories of \(R\) and \(A\), especially those involving actual or potential structures on \(A\) which ”stratify” its homological algebra. The original motivation comes from the theory of Schur algebras and the symmetric group, Lie theory, and the representation theory of finite dimensional algebras and finite groups.
The book synthesizes common features of many of the above areas, and presents a number of new directions. Included are an abstract ”Specht/Weyl module” correspondence, a new theory of stratified algebras, and a deformation theory for them. The approach reconceptualizes most of the modular representation theory of symmetric groups involving Specht modules and places that theory in a broader context. Finally, the authors formulate some conjectures involving the theory of stratified algebras and finite Coexeter groups, aiming toward understanding the modular representation theory of finite groups of Lie type in all characteristics.
Graduate students and research mathematicians interested in representation theory of algebraic and finite groups, finitedimensional algebras, and Lie algebras.

Chapters

Introduction

1. Preliminaries

2. Stratified algebras

3. Stratifying endomorphism algebras

4. Stratifications and orders in semisimple algebras

5. Examples

6. Some conjectures for finite Coxeter groups and further remarks