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arXiv · 2211.14195

A Gelfand-MacPherson correspondence for quiver moduli

Hans Franzen
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Abstract

We show that a semi-stable moduli space of representations of an acyclic quiver can be identified with two GIT quotients by reductive groups. One of a quiver Grassmannian of a projective representation, the other of a quiver Grassmannian of an injective representation. This recovers as special cases the classical Gelfand-MacPherson correspondence and its generalization by Hu and Kim to bipartite quivers, as well as the Zelevinsky map for a quiver of Dynkin type A with the linear orientation.

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Hans Franzen. 2022-11-25. A Gelfand-MacPherson correspondence for quiver moduli. https://arxiv.org/abs/2211.14195

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