Semi-invariants of mixed representations of quivers

Details Semi-invariants of mixed representations of quivers Semi-invariants of mixed representations of quivers

2005-12-30

arxiv.org/abs/math/0512651v4

Transform. Groups, 12 (2007), No. 2, 341-369

Mathematics

Representation Theory

37 pages; v2. notations are improved; v3. final version; v4. Now the numeration of statements is the same as in the printed ve

Scientific paper

The notion of mixed representations of quivers can be derived from ordinary quiver representations by considering the dual action of groups on "vertex" vector spaces together with the usual action. A generating system for the algebra of semi-invariants of mixed representations of a quiver is determined. This is done by reducing the problem to the case of bipartite quivers of the special form and by introducing a function DP on three matrices, which is a mixture of the determinant and two pfaffians.

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