Right q-Radial Calculus at Integral Superdimension
Abstract
We study the intrinsic right q-radial derivative at integral superdimension M=m−2n, using an independent formal parameter Q before the specialisation Q=qM. The exterior-blade action carries the parity factor (−1)|I|, and the corresponding Fischer theory uses right multiplication. We establish finite-support compatibility, faithful coordinate realisations in a sufficient finite-block range, and localised Green and determinant-localised Fischer decompositions. For one vector, we determine the kernel and cokernel explicitly, including the additional singular monomial and missing image exactly when M∈−2ℕ0. In degree zero the right Fischer operator is diagonal on auxiliary exterior blades, with eigenvalue [M−p]q+p at nonempty support rank p. For positive integral M, resonances in 0<q<1 occur exactly at ranks p>M: each rank has one simple resonance, these values increase strictly with p, and the corresponding kernels and singular right-monogenic elements are explicit. The two-vector Fischer determinant is nonzero for positive M and 0<q<1.
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BibTeX
@misc{boryreyes2026right,
title = {{Right $q$-Radial Calculus at Integral Superdimension}},
author = {Juan Bory-Reyes and Baruch Schneider and Diana Barseghyan Schneiderová and Yifan Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.14449},
eprint = {2607.14449},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.14449},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Right q-Radial Calculus at Integral Superdimension
AU - Juan Bory-Reyes
AU - Baruch Schneider
AU - Diana Barseghyan Schneiderová
AU - Yifan Zhang
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2607.14449
UR - https://arxiv.org/abs/2607.14449
AB - We study the intrinsic right q-radial derivative at integral superdimension M=m−2n, using an independent formal parameter Q before the specialisation Q=q^M. The exterior-blade action carries the parity factor (−1)^|I|, and the corresponding Fischer theory uses right multiplication. We establish finite-support compatibility, faithful coordinate realisations in a sufficient finite-block range, and localised Green and determinant-localised Fischer decompositions. For one vector, we determine the kernel and cokernel explicitly, including the additional singular monomial and missing image exactly when M∈−2ℕ_0. In degree zero the right Fischer operator is diagonal on auxiliary exterior blades, with eigenvalue [M−p]_q+p at nonempty support rank p. For positive integral M, resonances in 0<q<1 occur exactly at ranks p>M: each rank has one simple resonance, these values increase strictly with p, and the corresponding kernels and singular right-monogenic elements are explicit. The two-vector Fischer determinant is nonzero for positive M and 0<q<1.
ER -