Several integrals of quaternionic field on hyperbolic matrix space

TL;DR

This paper computes integrals and volume measures of hyperbolic matrix spaces over quaternionic fields, which are crucial for understanding kernel functions in these mathematical structures.

Contribution

It introduces new integral formulas and volume calculations for quaternionic hyperbolic matrix spaces, advancing the mathematical understanding of these structures.

Findings

Calculated integrals over quaternionic matrix spaces

Derived volume formulas for hyperbolic quaternionic matrix spaces

Facilitated kernel function computations for these spaces

Abstract

Some integrals of matrix spaces over a quaternionic field have been calculated in this work. The associated volume of hyperbolic matrix spaces over a quaternionic field has also been calculated by making use of these integrals, and it is of great significance in calculating related kernel functions of these spaces.