Abstract: Methods of Harder and Narasimhan from
the theory of moduli of vector bundles are applied to moduli of quiver
representations. Using the Hall algebra approach to quantum groups, an
analog of the Harder-Narasimhan
recursion is constructed inside the quantized enveloping algebra
of a Kac-Moody algebra. This leads to a canonical orthogonal system, the
HN system, in this algebra. Using a resolution of the recursion, an explicit
formula for the HN system is given. As an application, explicit formulas
for Betti numbers of the cohomology of quiver moduli are derived, generalizing
several results on the cohomology of quotients in 'linear algebra type'
situations. |
