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 $Q=q^M$. 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 $M\in -2{\mathbb{N}}_0$. 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 $0<q<1$.