{
  "abstract": "For a field $F$ we study the coinvariants for the $SL_n(F)$-action on the double Steinberg module $St_n(F) \\otimes St_n(F)$ and show they have a rich algebraic structure: for $n = 2$ it is the Grothendieck-Witt group of $F$, and for all $n$ they assemble to a graded nonunital $\\mathbb{Z}[F^\\times]$-algebra, whose rational (underived) indecomposables may be expressed in terms of the augmentation ideal of the Grothendieck-Witt group. We then explain, building on work of Galatius-Kupers-Randal-Williams, that the special linear groups $SL_n(F)$ assemble to an $E_\\infty$-algebra in a suitable functor category, whose $E_2$-homology groups have a vanishing line of slope 2 and on the critical line are given by the double Steinberg coinvariants.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39991",
  "author_total": 5,
  "authors": [
    {
      "name": "Tatiana Abdelnaim"
    },
    {
      "name": "David Chan"
    },
    {
      "name": "Alexander Kupers"
    },
    {
      "name": "Robin J. Sroka"
    },
    {
      "name": "Matthew Scalamandre"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4bs4mdyjg53hz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39991",
  "fulltext_url": null,
  "id": "4bs4mdyjg53hz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39991",
  "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.KT"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7215062603",
  "pdf_url": "https://arxiv.org/pdf/2609.39991",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4bs4mdyjg53hz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.39991",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39991"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.KT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Double Steinberg coinvariants for special linear groups",
  "title_text": "Double Steinberg coinvariants for special linear groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/4bs4mdyjg53hz",
  "venue": "arXiv",
  "versions": []
}