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Based on invited lectures at the 1992 Canadian Algebra Seminar, this volume represents an up-to-date and unique report on finite-dimensional algebras as a subject with many serious interactions with other mathematical disciplines, including algebraic groups and Lie theory, automorphic forms, sheaf theory, finite groups, and homological algebra. It will interest mathematicians and graduate students in these and related subjects as an introduction to research in an area of increasing relevance and importance.
List of contents
Equivalences of Blocks of Group Algebras.- On the Endomorphism Algebras of Gelfand-Graev Representations.- Harish-Chandra Vertices, Green Correspondence in Hecke Algebras, and Steinbergs Tensor Product Theorem in Nondescribing Characteristic.- On Tilting Modules and Invariants for Algebraic Groups.- Harish-Chandra Subalgebras and Gelfand-Zetlin Modules.- Algebras Associated to Bruhat Intervals and Polyhedral Cones.- Symmetric Groups and Quasi-Hereditary Algebras.- Quasitilted Algebras.- Tilting Theory and Differential Graded Algebras.- Wild Canonical Algebras and Rings of Automorphic Forms.- The Ext Algebra of a Highest Weight Category.- Coxeter transformations and the representation theory of algebras.- Translation Functors and Equivalences of Derived Categories for Blocks of Algebraic Groups.- Blocks with cyclic defect (Green orders).- Rigid and Exceptional Sheaves on a Del Pezzo Surface.- Quasihereditary algebras and Kazhdan-Lusztig theory.- Cycles in Module Categories.- Relative Homology.- Tilting Theory and Selfinjective Algebras.
Summary
Proceedings of the NATO Advanced Research Workshop on Representations of Algebras and Related Topics, Ottawa, Canada, August 10--18, 1992
