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Geometric Methods in Representation Theory I
Edited by: Michel Brion, Université Grenoble I, St. Martin d'Heres, France
A publication of the Société Mathématique de France.
cover
Séminaires et Congrès
2012; 361 pp; softcover
Number: 24
ISBN-13: 978-2-85629-356-0
List Price: US$105
Member Price: US$84
Order Code: SECO/24.1
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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 16-July 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, Kac-Moody 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 \(U_q(\widehat{\mathfrak{sl}}_n)\)
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