2007/08/31 by Kiyoshi Igusa, Kent Orr, Gordana Todorov +1 · 1 citation
Mathematics · #math.RT #math.RA #msc:16G20 #msc:13A50
paper · pdf · doi:10.1112/s0010437x09004151
34 pages
arxiv created 2008/10/11 · arxiv updated 2014/01/14
We define and study virtual representation spaces having both positive and negative dimensions at the vertices of a quiver without oriented cycles. We consider the natural semi-invariants on these spaces which we call virtual semi-invariants and prove that they satisfy the three basic theorems: the First Fundamental Theorem, the Saturation Theorem and the Canonical Decomposition Theorem. In the special case of Dynkin quivers with n vertices this gives the fundamental interrelationship between supports of the semi-invariants and the Tilting Triangulation of the (n-1)-sphere.