The Harder-Narasimhan system in quantum groups and cohomology of quiver moduli

Details The Harder-Narasimhan system in quantum groups and cohomology of quiver moduli The Harder-Narasimhan system in quantum groups and cohomology of quiver moduli

2002-04-04

arxiv.org/abs/math/0204059v1

Mathematics

Quantum Algebra

22 pages

Scientific paper

10.1007/s00222-002-0273-4

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.

Affiliated with

Also associated with

No associations

Rating

The Harder-Narasimhan system in quantum groups and cohomology of quiver moduli does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Harder-Narasimhan system in quantum groups and cohomology of quiver moduli, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Harder-Narasimhan system in quantum groups and cohomology of quiver moduli will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-640512