# Geometric methods in representation theory - Volume 1

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This first volume gathers part of the texts issued from the summer school "Geometric methods in representation theory" (Grenoble, 16 June -4 July, 2008). They are expanded versions of lecture notes for the courses of Bertin, Brion, Ginzburg, Gordon, Jantzen, and Leclerc ; the notes of Schiffmann's course appear in the second volume, as well as ten research or survey articles. 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 topics in algebraic geometry (punctual Hilbert schemes, geometric invariant theory, symplectic geometry,...), representation theory (quivers, Kac-Moody algebras, quantum groups,...), homological methods (intersection cohomology, equivariant cohomology...). The lecture notes include introductions to fundamental aspects of the domain : quiver representations, punctual Hilbert schemes, as well as more specialized texts on Nakajima varieties, Haiman's work, moment graphs and representation theory, representations in Fock space. 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.

 AUTEUR Michel Brion DATE DE PUBLICATION 2013-Apr-01 TAILLE DU FICHIER 7,53 MB

Geometric Methods in Representation Theory | Mathematics

Chapter 1 Planar graphs and polytopes 1.1 Planar graphs A graph G = (V;E) is planar, if it can be drawn in the plane so that its edges are Jordan curves and they intersect only at their endnodes1.A plane map is a planar graph with a ﬂxed embedding. We also use this phrase to denote the image of this embedding, i.e., the

International Journal of Geometric Methods in Modern Physics

GEOMETRIC FUNCTION THEORY DAVID BEN-ZVI Dear Cafe Patrons, In this guest post I want to brieﬂy discuss correspondences, integral transforms and their cate-goriﬁcation as they apply to representation theory, a topic that might be called geometric function theory. This has been one of the fundamental paradigms of geometric representation theory (to-gether with localization of representations ...

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