{
  "abstract": "We develop a discrete $q$-Hermitian Clifford calculus based on coordinatewise Jackson differences on multiplicative $q$-lattices. The resulting Hermitian Jackson--Dirac operators are nilpotent, factor a $q$-Laplacian, and have occupancy-dependent Euler anticommutators. These give explicit Fischer projectors and homotopies, but the local calculus is not controlled by total degree. We prove a two-face Cauchy--Kovalevskaya theorem for polynomials and extend it to a $q$-analytic Jackson--Fischer class. A divided-power conjugation recovers scalar Euler relations and transfers the classical joint Fischer decomposition and dimension formulas. The Jackson--Fischer completion is a vector-valued $q$-Fock space whose polarized nullspaces have projected reproducing kernels; the joint kernel is obtained by alternating projections. We also determine the linear symmetry group of the multiplicative lattice.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15459",
  "author_total": 3,
  "authors": [
    {
      "name": "Baruch Schneider"
    },
    {
      "name": "Diana Schneiderová"
    },
    {
      "name": "Yifan Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5md18fd0301ze.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15459",
  "fulltext_url": null,
  "id": "5md18fd0301ze",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15459",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CV"
    ],
    [
      "openalex",
      "2604|Algebraic and Geometric Analysis"
    ]
  ],
  "openalex": "W7213252426",
  "pdf_url": "https://arxiv.org/pdf/2609.15459",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5md18fd0301ze.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.15459",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15459"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Discrete q-Hermitian Clifford analysis",
  "title_text": "Discrete q-Hermitian Clifford analysis",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/5md18fd0301ze",
  "venue": "arXiv",
  "versions": []
}