Stratifying Endomorphism Algebras (Memoirs of the American Mathematical Society, 591) - Softcover

Cline, Edward; Parshall, Brian; Scott, Leonard L.

Softcover

ISBN 10: 082180488X ISBN 13: 9780821804889

Publisher: Amer Mathematical Society, 1996

Synopsis

Suppose that $R$ is a finite dimensional algebra and $T$ is a right $R$-module. Let $A = \textnormal{ End}_R(T)$ 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.

Edition details

• Publisher: Amer Mathematical Society
• Publication date: 1996
• Language: English
• ISBN 10: 082180488X
• ISBN 13: 9780821804889
• Binding: Paperback
• Number of pages: 119