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Abstract:
I define virtual representation spaces having both positive
and negative dimensions at the vertices of a quiver without oriented
cycles. I consider the natural semi-invariants on these spaces called
virtual semi-invariants. 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. This is a joint work with K. Igusa, K. Orr and G. Todorov.
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