PreprintCC BY 4.0arXiv
A short note on Arthur parameters with singular orbit closures
Abstract
This short article resolves a question about Arthur parameters highlighted in previous work of Balodis, Cunningham, Fiori and Zhang, in the case of GLn/F where F/ℚp is a p-adic field. Namely, we prove that every Arthur parameter ψ of GLn/F, can be factored into Arthur parameters ψ≅ ψ1⊕⋯ ⊕ψr such that the orbit Cψ=Cψ1×⋯× Cψr⊆ Vλψ1× ⋯ × Vλψr in the associated Vogan variety has smooth closure if and only if each C̅ψi is smooth for i=1, …, r, and that Cψi has smooth closure if and only if it is open or closed.
Related
- Geometric structures, orbit closures and invariant measures in moduli spaces
- Finite group actions on the non-minimal nilpotent orbit closures in type A
- Singularities of orbit closures in loop spaces of symmetric varieties II: twisted cases
- An order-reversing embedding of Turing degrees into Arthur-Nimue-Merlin degrees (short version)
- Legendrian families of lines on nilpotent orbit closures
BibTeX
@misc{balodis2026short,
title = {{A short note on Arthur parameters with singular orbit closures}},
author = {Kristaps John Balodis},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06793},
eprint = {2609.06793},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06793},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A short note on Arthur parameters with singular orbit closures
AU - Kristaps John Balodis
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2609.06793
UR - https://arxiv.org/abs/2609.06793
AB - This short article resolves a question about Arthur parameters highlighted in previous work of Balodis, Cunningham, Fiori and Zhang, in the case of GL_n/F where F/ℚ_p is a p-adic field. Namely, we prove that every Arthur parameter ψ of GL_n/F, can be factored into Arthur parameters ψ≅ ψ_1⊕⋯ ⊕ψ_r such that the orbit C_ψ=C_ψ_1×⋯× C_ψ_r⊆ V_λ_ψ_1× ⋯ × V_λ_ψ_r in the associated Vogan variety has smooth closure if and only if each C̅_ψ_i is smooth for i=1, …, r, and that C_ψ_i has smooth closure if and only if it is open or closed.
ER -