{
  "abstract": "We use the connective formal group law to define a one-parameter ($β$-)deformation of the motivic Segre classes of Schubert cells in the $d$-step flag variety. This $β$-deformation specializes to the motivic Segre classes of Schubert cells when $β=1$ and to the Segre-Schwartz-MacPherson classes of Schubert cells when $β=0$ (though the $β$-deformations are not simply the $β$-homogenizations of the motivic Segre classes). We define rational function representatives for the $β$-deformed classes in the $d=1$ case in terms of a solvable lattice model, and we prove a combinatorial formula for the structure constants in the $β$-deformed basis in the $d=1$ case using Knutson-Tao puzzles. Unexpectedly, the structure constants are built out of entries of $R$-matrices for the multi-parameter quantum group of type $\\widehat{a}_2$ (which suggests an action of multi-parameter quantum groups on equivariant connective $K$-rings of Nakajima quiver varieties, with their convolution algebra structures). We show that our $β$-deformations arise from canonical elements in a quotient of the torus-equivariant algebraic cobordism ring of the cotangent bundle of the flag variety by proving that the canonical elements satisfy a GKM type condition (in future work, we will show that these canonical elements also lie in the torus-equivariant connective $K$-ring, in the sense of Karpenko--Merkurjev, of this cotangent bundle).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.26556",
  "author_total": 1,
  "authors": [
    {
      "name": "Raj Gandhi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/60zhkartj13tp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.26556",
  "fulltext_url": null,
  "id": "60zhkartj13tp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.26556",
  "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.AT"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7162525319",
  "pdf_url": "https://arxiv.org/pdf/2605.26556",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/60zhkartj13tp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2605.26556",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.26556"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Motivic Segre classes of Schubert cells and the connective formal group law",
  "title_text": "Motivic Segre classes of Schubert cells and the connective formal group law",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/60zhkartj13tp",
  "venue": "arXiv",
  "versions": []
}