{
  "abstract": "For irreducible components $C_σ$ of Lusztig's nilpotent varieties of type $A$ with graded dimension $(1,2,\\dots,n,n-1,\\dots,1)$ arising from permutations $σ\\in S_n$, we characterize the property that $C_σ\\oplus C_σ$ is an irreducible component combinatorially in terms of $σ$. The permutations that occur, which we call \\emph{pseudosmooth}, are described by a recursion on direct sums and deleting suitable corners, whose terminal cases are the permutations obtained from \\[ 3412,\\quad 4231,\\quad 35142,\\quad 42513,\\quad 45312,\\quad 426153,\\quad 463152,\\quad 526413 \\] by inflating the entries into consecutive decreasing blocks. The main new input is a hereditary property valid for decompositions of multisegments with disjoint extreme points.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06601",
  "author_total": 2,
  "authors": [
    {
      "name": "Erez Lapid"
    },
    {
      "name": "Mark Shusterman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/17s60y30b4hcp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06601",
  "fulltext_url": null,
  "id": "17s60y30b4hcp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06601",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7212006465",
  "pdf_url": "https://arxiv.org/pdf/2609.06601",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/17s60y30b4hcp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06601",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06601"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A hereditary theorem for rigid and pseudorigid components of Lusztig's nilpotent varieties in type $A$",
  "title_text": "A hereditary theorem for rigid and pseudorigid components of Lusztig's nilpotent varieties in type A",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/17s60y30b4hcp",
  "venue": "arXiv",
  "versions": []
}