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.
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}
}