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Multiplicative properties of projectively dual varieties.

Andrei Zelevinsky; Jerzy Weyman — 1994

Manuscripta mathematica

Generalized quivers associated to reductive groups

Harm Derksen; Jerzy Weyman — 2002

Colloquium Mathematicae

We generalize the definition of quiver representation to arbitrary reductive groups. The classical definition corresponds to the general linear group. We also show that for classical groups our definition gives symplectic and orthogonal representations of quivers with involution inverting the direction of arrows.

Singularities of hyperdeterminants

Jerzy Weyman; Andrei Zelevinsky — 1996

Annales de l'institut Fourier

We study the singular locus of the variety of of an arbitrary format. Our main result is a classification of irreducible components of the singular locus. Equivalently, we classify irreducible components of the singular locus for the projectively dual variety of a product of several projective spaces taken in the Segre embedding.

The combinatorics of quiver representations

Harm Derksen; Jerzy Weyman — 2011

Annales de l’institut Fourier

We give a description of faces, of all codimensions, for the cones spanned by the set of weights associated to the rings of semi-invariants of quivers. For a triple flag quiver and its faces of codimension 1 this description reduces to the result of Knutson-Tao-Woodward on the facets of the Klyachko cone. We give new applications to Littlewood-Richardson coefficients, including a product formula for LR-coefficients corresponding to triples of partitions lying on a wall of the Klyachko cone. We systematically...

The existence of equivariant pure free resolutions

David Eisenbud; Gunnar Fløystad; Jerzy Weyman — 2011

Annales de l’institut Fourier

Let $A = K [x_{1}, \dots, x_{m}]$ be a polynomial ring in $m$ variables and let $d = (d_{0} < \dots < d_{m})$ be a strictly increasing sequence of $m + 1$ integers. Boij and Söderberg conjectured the existence of graded $A$ -modules $M$ of finite length having pure free resolution of type $d$ in the sense that for $i = 0, \dots, m$ the $i$ -th syzygy module of $M$ has generators only in degree $d_{i}$ . This paper provides a construction, in characteristic zero, of modules with this property that are also $G L (m)$ -equivariant. Moreover, the construction works over...

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