Dipartimento di Scienze di Base e Applicate per l'Ingegneria

Seminario di Geometria

Aula 1B1, pal. RM002

Jerzy Weyman (University of Connecticut)

Quiver representations and their semi-invariants

Abstract:
In this talk I will discuss the basic notions related to quiver
representations. A quiver is just a directed graph, its representation is
assigning a vector space to each vertex and a linear map to each arrow.
One studies the structure of representations of a given quiver. I will
discuss Gabriel Theorem which classifies quivers for which there are only
finitely many indecomposable representations. In more complicated cases
one needs geometric methods, which involves rings of semi-invariants with
respect to groups of coordinate changes at each vertex. I will describe
some applications including an application to describing tensor product
multiplicities of irreducible representations of general linear groups.