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Quivers with potentials and their representations I: Mutations
- H. Derksen, J. Weyman, A. Zelevinsky
- Mathematics
- 4 April 2007
Abstract.We study quivers with relations given by noncommutative analogs of Jacobian ideals in the complete path algebra. This framework allows us to give a representation-theoretic interpretation of…
Schur Functors and Schur Complexes
- K. Akin, D. Buchsbaum, J. Weyman
- Mathematics
- 1 June 1982
Quivers with potentials and their representations II: Applications to cluster algebras
- H. Derksen, J. Weyman, A. Zelevinsky
- Mathematics
- 4 April 2009
We continue the study of quivers with potentials and their representations initiated in the first paper of the series. Here we develop some applications of this theory to cluster algebras. As shown…
Cohomology of Vector Bundles and Syzygies
- J. Weyman
- Mathematics
- 1 June 2003
1. Introduction 2. Schur functions and Schur complexes 3. Grassmannians and flag varieties 4. Bott's theorem 5. The geometric technique 6. The determinantal varieties 7. Higher rank varieties 8. The…
Semi-invariants of quivers and saturation for Littlewood-Richardson coefficients
- H. Derksen, J. Weyman
- Mathematics
- 13 March 2000
Σ(Q,α) is defined in the space of all weights by one homogeneous linear equation and by a finite set of homogeneous linear inequalities. In particular the set Σ(Q,α) is saturated, i.e., if nσ ∈…
The combinatorics of quiver representations
- H. Derksen, J. Weyman
- Mathematics
- 11 August 2006
We give a description of faces of all codimensions for the cones of weights of rings of semi-invariants of quivers. For a triple flag quiver and faces of codimension 1 this reduces to the result of…
Graded Characters of Modules Supported in the Closure of a Nilpotent Conjugacy Class
- M. Shimozono, J. Weyman
- MathematicsEur. J. Comb.
- 7 April 1998
This is a combinatorial study of the Poincare polynomials of isotypic components of a natural family of graded GL(n)-modules supported in the closure of a nilpotent conjugacy class. These polynomials…
On the Canonical Decomposition of Quiver Representations
- H. Derksen, J. Weyman
- MathematicsCompositio Mathematica
- 1 September 2002
Kac introduced the notion of the canonical decomposition for a dimension vector of a quiver. Here we will give an efficient algorithm to compute the canonical decomposition. Our study of the…
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