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Junior Geometry
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Alberto San Miguel, : Quivers and their Representations
Tuesday, March 02, 2021, 03:45pm - 04:45pm
Quivers are another name for directed graphs. In this talk we will define what a quiver representation is and explain some basic results, constructions, and examples of them. One major result is Gabriel's theorem, which says that a quiver has finitely many indecomposable representations if and only if it is a simply laced Dynkin diagram. We will explain how these indecomposable representations are in bijection with the positive roots of the corresponding simple lie algebra. Finally we will construct quiver varieties as a way to describe the space of representations of a quiver and show how the Springer resolution in type A appears as an example.

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