English

A Gelfand-MacPherson correspondence for quiver moduli

Algebraic Geometry 2022-11-28 v1 Representation Theory

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.

Keywords

Cite

@article{arxiv.2211.14195,
  title  = {A Gelfand-MacPherson correspondence for quiver moduli},
  author = {Hans Franzen},
  journal= {arXiv preprint arXiv:2211.14195},
  year   = {2022}
}

Comments

28 pages, comments are welcome

R2 v1 2026-06-28T07:12:50.317Z