Séminaires et Congrès 2012; 361 pp; softcover Number: 24 ISBN13: 9782856293560 List Price: US$105 Member Price: US$84 Order Code: SECO/24.1
 This volume contains the expanded versions of lecture notes and of some seminar talks presented at the 2008 Summer School, Geometric Methods in Representation Theory, which was held in Grenoble, France, from June 16July 4, 2008. They give an overview of representation theory of quivers, chiefly from a geometric perspective. The methods and results cover a wide range of topics in algebraic geometry (punctual Hilbert schemes, geometric invariant theory, symplectic geometry), representation theory (Hall algebras, KacMoody algebras, quantum groups), homological methods (intersection cohomology, equivariant cohomology, derived categories of coherent sheaves). The lecture notes include introductory texts to fundamental aspects of the domain: quiver representations, punctual Hilbert schemes, Hall algebras, as well as more specialized texts on Nakajima varieties, Haiman's work, moment graphs and representations, canonical and crystal bases of Hall algebras, and representations in Fock spaces. The ten articles cover recent advances in various directions. In view of the diverseness of the topics, the reader is invited to consult the introductions of the texts for detailed overviews of their respective contents. A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list. Readership Graduate students and research mathematicians. Table of Contents  J. Bertin  The punctual Hilbert scheme: An introduction
 M. Brion  Representations of quivers
 V. Ginzburg  Lectures on Nakajima's quiver varieties
 I. Gordon  Haiman's work on the n! theorem, and beyond
 J. C. Jantzen  Moment graphs and representations
 B. Leclerc  Fock space representations of \(U_q(\widehat{\mathfrak{sl}}_n)\)
