Regular loci of affine Springer fibers at very special parahoric level

For split groups, we prove that centralizers act transitively on regular loci of affine Springer fibers at very special parahoric level. As an application, we prove Chi's conjecture on the number of top-dimensional irreducible components of affine Lusztig varieties.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-11-10
DOI
https://doi.org/10.48550/arxiv.2611.13601
Primary Topic
Advanced Algebra and Geometry
Type
preprint
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preprint

Regular loci of affine Springer fibers at very special parahoric level

Ryosuke Shimada
arXiv (Cornell University)
Advanced Algebra and Geometry
preprint

Regular loci of affine Springer fibers at very special parahoric level

Ryosuke Shimada
preprint en

Abstract

For split groups, we prove that centralizers act transitively on regular loci of affine Springer fibers at very special parahoric level. As an application, we prove Chi's conjecture on the number of top-dimensional irreducible components of affine Lusztig varieties.

arXiv (Cornell University)
Advanced Algebra and Geometry
DOIOpen Access PDFOpenAlex
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Regular loci of affine Springer fibers at very special parahoric level — Ryosuke Shimada · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS