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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

International Journal of Geometric Methods in Modern Physics

motivating geometric representation theory. Ask Question Asked 6 years, 11 months ago. Active 6 years, 11 months ago. Viewed 5k times 22. 17 $\begingroup$ I am wondering if there is a good motivation for geometric representation theory from within the questions of classical representation theory. In other words, I'd be curious to see something using geometry that is "meatier" than, say, just ...

Methods of Representation Theory: With Applications to ...

Title: Geometric Methods in Representation Theory. Authors: Kari Vilonen (Submitted on 2 Oct 2004) Abstract: These myh lectures at the Park City conference in 1998. Subjects: Representation Theory (math.RT); Algebraic Geometry (math.AG) MSC classes: 22E46: Journal reference: Representation theory of Lie groups (Park City, UT, 1998), 241--290, IAS/Park City Math. Ser., 8, Amer. Math. Soc ...

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