Pascal algebra of matrices and Pascal map on jet bundles

TL;DR

This paper introduces a Pascal-type matrix algebra and a canonical Pascal map on jet bundles, providing an intrinsic way to define point-wise contact between Hermitian vector bundles through unitary equivalence.

Contribution

It identifies a new matrix algebra and defines the Pascal map on jet bundles, offering an intrinsic characterization of contact between Hermitian vector bundles.

Findings

Defined a Pascal-type matrix algebra.

Established the Pascal map as a canonical bundle map.

Provided an intrinsic definition of point-wise contact.

Abstract

We identify and study a matrix algebra consisting of Pascal-type matrices. The generator of the matrix algebra is shown to well define a canonical bundle map, called the Pascal map on jet bundles, and we use it to give an intrinsic definition of point-wise contact between Hermitian vector bundles in terms of unitary equivalence of the Pascal maps.