Symmetric degenerations are not in general induced by type A degenerations
| Autor: | Magdalena Boos, Giovanni Cerulli Irelli |
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| Jazyk: | English<br />French<br />Italian |
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Rendiconti di Matematica e delle Sue Applicazioni, Vol 43, Iss 1-2, Pp 133-149 (2022) |
| Druh dokumentu: | article |
| ISSN: | 1120-7183 2532-3350 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
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