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Title: A conjectural description for real Schur roots of acyclic quivers
Speaker: Kyu-Hwan Lee (University of Connecticut)
Time: Friday, March 24, 2017 at 3:00 pm
Place: Mont 214Abstract: The dimension vectors of indecomposable rigid representations of an acyclic quiver are called real Schur roots. Real Schur roots are important in understanding representations of quivers and they also appear in the denominators of non-initial cluster variables in the theory of cluster algebras. However, it seems difficult to describe real Schur roots in a concrete way that distinguishes them among all positive real roots. In this talk, we will give a conjectural description for real Schur roots of acyclic quivers using non-self-intersecting paths on punctured Riemann surfaces, and prove it for rank 3 quivers with multiple arrows between every pair of vertices. Each of such paths gives rise to a reflection of the Weyl group of the corresponding Kac--Moody algebra and determines a real Schur root uniquely. This is a collaboration with Kyungyong Lee.
Organizer Ralf Schiffler