Discrete q-Hermitian Clifford analysis

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.

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BibTeX RIS

BibTeX

@misc{schneider2026discrete,
  title = {{Discrete q-Hermitian Clifford analysis}},
  author = {Baruch Schneider and Diana Schneiderová and Yifan Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.15459},
  eprint = {2609.15459},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.15459},
  note = {CC BY-NC-ND 4.0},
}

RIS

TY  - UNPB
TI  - Discrete q-Hermitian Clifford analysis
AU  - Baruch Schneider
AU  - Diana Schneiderová
AU  - Yifan Zhang
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.15459
UR  - https://arxiv.org/abs/2609.15459
AB  - 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.
ER  -

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