{
  "abstract": "The Type D asymmetric simple exclusion process (ASEP), a particle system involving two classes of particles, was studied from both probabilistic and algebraic perspectives by Kuan et al. (2022). From a probabilistic perspective, we perform stochastic fusion on the Type D ASEP introduced by Kuan (2019) and analyze the outcome on the generator matrix, limits of drift speed, stationary distributions, and Markov self-duality. From an algebraic perspective, we construct a fused Type D ASEP system from a Casimir element of $\\mathcal{U}_q(\\mathfrak{so}_6)$, using crystal bases to analyze and manipulate various representations of $\\mathcal{U}_q(\\mathfrak{so}_6)$. We know that the same generators for the normal ASEP are produced by stochastic fusion and by a suitable ground state transformation on a central element of $\\mathcal{U}_q(\\mathfrak{sl}_2)$ in a symmetric tensor product representation. However, in the case of the Type D ASEP, we find that the probabilistic and algebraic generator matrices are not the same and thus represent different processes. We conclude that the relationship between stochastic fusion and a ground state transformation (specifically, what we term the Type A ground state transformation) established by Kuan (2019) does not generalize to all finite-dimensional simple Lie algebras.",
  "abstract_shown": true,
  "affiliations": [
    "Cornell University, USA",
    "Princeton University, USA",
    "University of Michigan, USA"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Erik Brodsky"
    },
    {
      "affs": [
        1
      ],
      "name": "Eva Engel"
    },
    {
      "affs": [
        0
      ],
      "name": "Connor Panish"
    },
    {
      "affs": [
        2
      ],
      "name": "Lillian Stolberg"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fg1pzge8mr2br.bib",
  "cited_by": 0,
  "doi": "10.3842/sigma.2026.095",
  "fulltext_url": null,
  "id": "fg1pzge8mr2br",
  "issns": [
    "1815-0659"
  ],
  "landing_url": "https://sigma-journal.com/2026/095/",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W4401203429",
  "pdf_url": "https://sigma-journal.com/2026/095/sigma26-095.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": "SIGMA (Symmetry, Integrability and Geometry: Methods and Application)",
  "ris": "https://research.draconitic.com/paper/fg1pzge8mr2br.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:27Z",
      "native_id": "10.3842/sigma.2026.095",
      "source": "crossref",
      "url": "https://sigma-journal.com/2026/095/"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2610|Stochastic processes and statistical mechanics",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Comparative Analyses of the Type D ASEP: Stochastic Fusion and Crystal Bases",
  "title_text": "Comparative Analyses of the Type D ASEP: Stochastic Fusion and Crystal Bases",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:27Z",
  "url": "https://research.draconitic.com/paper/fg1pzge8mr2br",
  "venue": "Symmetry, Integrability and Geometry: Methods and Applications",
  "versions": []
}