Horn conditions for quiver subrepresentations and the moment map

Open Access
Authors
Publication date 2023
Journal Pure and Applied Mathematics Quarterly
Article number 1
Volume | Issue number 19 | 4
Pages (from-to) 1687-1731
Number of pages 45
Organisations
  • Faculty of Science (FNWI) - Institute of Physics (IoP) - Institute for Theoretical Physics Amsterdam (ITFA)
  • Faculty of Science (FNWI) - Korteweg-de Vries Institute for Mathematics (KdVI)
  • Interfacultary Research - Institute for Logic, Language and Computation (ILLC)
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 = ΠxGL(nx) associated to a quiver and a dimension vector n = (nx).
Document type Article
Note In Special Issue in honor of Victor Guillemin
Language English
Published at https://doi.org/10.48550/arXiv.1901.07194 https://doi.org/10.4310/PAMQ.2023.V19.N4.A1
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1901.07194 (Accepted author manuscript)
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