Recursive Construction for a Class of Radial Functions II - Superspace

TL;DR

This paper extends recursion formulas for matrix Bessel functions to superspace, specifically for the unitary orthosymplectic supergroup, enabling explicit computations for supermatrices up to 8x8 dimensions.

Contribution

It introduces a new technique to extend recursion formulas to superspace, providing explicit results for supermatrices up to 8x8 dimensions.

Findings

Explicit recursion formulas for superspace matrix Bessel functions.

Feasibility of computations up to 8x8 supermatrices.

Introduction of a novel technique for superspace analysis.

Abstract

We extend the recursion formula for matrix Bessel functions, which we obtained previously, to superspace. It is sufficient to do this for the unitary orthosymplectic supergroup. By direct computations, we show that fairly explicit results can be obtained, at least up to dimension $8\times 8$ for the supermatrices. Since we introduce a new technique, we discuss various of its aspects in some detail.