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Geometric Methods in Representation Theory II
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; 456 pp; softcover
Number: 24
ISBN-13: 978-2-85629-361-4
List Price: US$105
Member Price: US$84
Order Code: SECO/24.2
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This second volume contains expanded versions of lecture notes for O. Schiffman's course, as well as ten research or survey articles, presented at the 2008 Summer School, Geometric Methods in Representation Theory (Grenoble, France, June 16-July 4, 2008).

These texts give an overview of the representation theory of quivers, chiefly from a geometric perspective. The methods and results cover a wide range of mathematical domains: algebra and representation theory (Hall algebras, canonical and crystal bases, cluster categories, modular representations), algebraic geometry (flag varieties, moduli spaces, symplectic singularities), and homological methods (perverse sheaves, exceptional collections). 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 interested in representation theory of quivers from a geometric perspective.

Table of Contents

  • O. Schiffmann -- Lectures on Hall algebras
  • O. Schiffmann< -- Lectures on canonical and crystal bases of Hall algebras
  • K. Baur -- Cluster categories, m-cluster categories and diagonals in polygons
  • A. Boralevi -- On simplicity and stability of the tangent bundle of rational homogeneous varieties
  • L. Evain -- Intersection theory on punctual Hilbert schemes and graded Hilbert schemes
  • D. Juteau, C. Mautner, and G. Williamson -- Perverse sheaves and modular representation theory
  • I. Losev -- On the structure of the category \(O\) for \(W\)-algebras
  • M. Perling< -- Examples for exceptional sequences of invertible sheaves on rational surfaces
  • O. Serman< -- Orthogonal and symplectic bundles on curves and quiver representations
  • D. A. Shmelkin -- Some remarks on Nakajima's quiver varieties of type A
  • M. Lehn and C. Sorger -- A symplectic resolution for the binary tetrahedral group
  • F. Vaccarino< -- Moduli of linear representations, symmetric products and the non commutative Hilbert scheme
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