Memoirs of the American Mathematical Society 1996; 119 pp; softcover Volume: 124 ISBN10: 082180488X ISBN13: 9780821804889 List Price: US$43 Individual Members: US$25.80 Institutional Members: US$34.40 Order Code: MEMO/124/591
 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. Readership Graduate students and research mathematicians interested in representation theory of algebraic and finite groups, finitedimensional algebras, and Lie algebras. Table of Contents  Preliminaries
 Stratified algebras
 Stratifying endomorphism algebras
 Stratifications and orders in semisimple algebras
 Examples
 Some conjectures for finite Coxeter groups and further remarks
 References
