We consider a symmetric quiver with relations. Its (symmetric) representations of a fixed symmetric dimension vector are encoded in the (symmetric) representation varieties. The orbits by a (symmetric) base change group action are the isomorphism classes of (symmetric) representations. The symmetric orbits are induced by simply restricting the non-symmetric orbits. However, when it comes to orbit closure relations, it is so far an open question under which assumptions they are induced. In connection with Borel orbits of 2-nilpotent matrices of classical Lie algebras, we describe an explicit example of a quiver of finite representation type for which orbit closure relations are induced in types B and C, but not in type D.
Symmetric degenerations are not in general induced by type A degenerations / Boos, Magdalena; CERULLI IRELLI, Giovanni. - In: RENDICONTI DI MATEMATICA E DELLE SUE APPLICAZIONI. - ISSN 2532-3350. - 43:(2022), pp. 133-149.
Symmetric degenerations are not in general induced by type A degenerations
Giovanni Cerulli Irelli
2022
Abstract
We consider a symmetric quiver with relations. Its (symmetric) representations of a fixed symmetric dimension vector are encoded in the (symmetric) representation varieties. The orbits by a (symmetric) base change group action are the isomorphism classes of (symmetric) representations. The symmetric orbits are induced by simply restricting the non-symmetric orbits. However, when it comes to orbit closure relations, it is so far an open question under which assumptions they are induced. In connection with Borel orbits of 2-nilpotent matrices of classical Lie algebras, we describe an explicit example of a quiver of finite representation type for which orbit closure relations are induced in types B and C, but not in type D.File | Dimensione | Formato | |
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