English

On degenerations and extensions of symplectic and orthogonal quiver representations

Representation Theory 2025-04-18 v1 Algebraic Geometry

Abstract

We discuss degenerations of symplectic and orthogonal representations of symmetric quivers and algebras with self-dualities. As in the non-symmetric case, we define a partial ordering, that we call symmetric Ext-order which gives a sufficient criterion for a symmetric degeneration. Then a detailed discussion of type A quivers and their (symmetric) representation theory via Auslander-Reiten theory leads to our main theorem which states that the symmetric degeneration order of a symmetric quiver of finite type is induced by the usual degeneration order between representations of the underlying quiver.

Keywords

Cite

@article{arxiv.2106.08666,
  title  = {On degenerations and extensions of symplectic and orthogonal quiver representations},
  author = {Magdalena Boos and Giovanni Cerulli Irelli},
  journal= {arXiv preprint arXiv:2106.08666},
  year   = {2025}
}

Comments

40 pages, 1 figure