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.

On degenerations and extensions of symplectic and orthogonal quiver representations / Cerulli Irelli, Giovanni; Boos, Magdalena. - In: ARKIV FÖR MATEMATIK. - ISSN 0004-2080. - 63:(2025), pp. 61-115. [10.4310/ARKIV.2025.v63.n1.a3]

On degenerations and extensions of symplectic and orthogonal quiver representations

Giovanni Cerulli Irelli
;
2025

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.
2025
QUIVER REPRESENTATIONS; DEGENERATION ORDER;
01 Pubblicazione su rivista::01a Articolo in rivista
On degenerations and extensions of symplectic and orthogonal quiver representations / Cerulli Irelli, Giovanni; Boos, Magdalena. - In: ARKIV FÖR MATEMATIK. - ISSN 0004-2080. - 63:(2025), pp. 61-115. [10.4310/ARKIV.2025.v63.n1.a3]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1731988
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