English

Normality of closure of orthogonal nilpotent symmetric orbits

Combinatorics 2022-05-11 v3 Algebraic Geometry Representation Theory

Abstract

We study closures of conjugacy classes in the symmetric matrices of the orthogonal group and we determine which one are normal varieties. In contrast to the result for the symplectic group where all classes have normal closure, there is only a relatively small portion of classes with normal closure. We perform a combinatorial computation on top of the same methods used by Kraft-Procesi and Ohta.

Keywords

Cite

@article{arxiv.2105.08680,
  title  = {Normality of closure of orthogonal nilpotent symmetric orbits},
  author = {Marco Trevisiol},
  journal= {arXiv preprint arXiv:2105.08680},
  year   = {2022}
}

Comments

22 pages, comments welcome. Part of my phd thesis. In version 2 I fix a typo in equation (4) and I explained better the justification of that equation. Version 3 includes the corrections suggested by the reviewers