On the Null Cone for Quiver Representations Under Reflection Functors

摘要

Let d be a prehomogeneous dimension vector for a connected quiver Q with the property that c~?d has a negative entry for some ~? ∈ □ where c is the Coxeter transformation corresponding to an admissible numbering of the vertices Q_0 of Q. Denote by rep(Q, d) the variety of d-dimensional representations of Q and by Sl(d) the product of the special linear groups at all vertices Q_0. We show how to find the irreducible components of the null cone of the algebraic quotient rep(Q, d)//Sl(d).