English

Extension-orthogonal components of nilpotent varieties

Representation Theory 2019-03-05 v1 Quantum Algebra

Abstract

Let Q be a Dynkin quiver, and let P(Q) be the corresponding preprojective algebra. Let I be a set of pairwise different indecomposable irreducible components of varieties of P(Q)-modules such that generically there are no extensions between these components. We show that the number of elements in I is at most the number of positive roots of Q. Furthermore, we give a module theoretic interpretation of Leclerc's counterexample to a conjecture of Berenstein and Zelevinsky.

Keywords

Cite

@article{arxiv.math/0208209,
  title  = {Extension-orthogonal components of nilpotent varieties},
  author = {Christof Geiß and Jan Schröer},
  journal= {arXiv preprint arXiv:math/0208209},
  year   = {2019}
}
R2 v1 2026-07-22T16:47:17.353Z