Volume 43_2_(2022)_133-149

Symmetric degenerations are not in general induced by type A degenerations
Magdalena Boos, Giovanni Cerulli Irelli

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

Rend. Mat. Appl. (7) 43 (2022) 133-149;  pdf