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.

TÉLÉCHARGER
AUTEUR Michel Brion
DATE DE PUBLICATION 2013-Apr-01
TAILLE DU FICHIER 3,96 MB
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This book emphasizes that the theory of representations is a good example of the use of algebraic and geometric methods in functional analysis, in which transformations are performed not on the points of a space, but on the functions defined on it. The topics discussed include Radon transform on a real affine space, integral transforms in the complex domain, and representations of the group of ...

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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 ...

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