Rendiconti di Matematica e delle Sue Applicazioni (Feb 2022)

Symmetric degenerations are not in general induced by type A degenerations

  • Magdalena Boos,
  • Giovanni Cerulli Irelli

Journal volume & issue
Vol. 43, no. 1-2
pp. 133 – 149

Abstract

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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.

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