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