Horn conditions for quiver subrepresentations and the moment map

Velleda Baldoni; Michèle Vergne; Michael Walter

doi:10.4310/PAMQ.2023.v19.n4.a1

Horn conditions for quiver subrepresentations and the moment map

Algebraic Geometry 2023-12-05 v5 Representation Theory Symplectic Geometry

Authors: Velleda Baldoni , Michèle Vergne , Michael Walter

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Abstract

We give inductive conditions that characterize the Schubert positions of subrepresentations of a general quiver representation. Our results generalize Belkale's criterion for the intersection of Schubert varieties in Grassmannians and refine Schofield's characterization of the dimension vectors of general subrepresentations. This implies Horn type inequalities for the moment cone associated to the linear representation of the group $G=\prod_x \operatorname{GL}(n_x)$ associated to a quiver and a dimension vector $\mathbf n=(n_x)$ .

Keywords

quiver representation subrepresentation schubert position moment map horn inequalities moment cone

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@article{arxiv.1901.07194,
  title  = {Horn conditions for quiver subrepresentations and the moment map},
  author = {Velleda Baldoni and Michèle Vergne and Michael Walter},
  journal= {arXiv preprint arXiv:1901.07194},
  year   = {2023}
}

Comments

44 pages, contains detailed proofs of results previously announced in arXiv:1804.00431; v4: dedicated to Victor Guillemin, references added

Horn conditions for quiver subrepresentations and the moment map

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