Proper holomorphic polynomial maps between bounded symmetric domains of classical type

TL;DR

This paper establishes a criterion for when two proper holomorphic polynomial maps between classical bounded symmetric domains are equivalent, based on their isotropic equivalence, enhancing understanding of their structure.

Contribution

It proves that proper holomorphic polynomial maps preserving the origin are equivalent if and only if they are isotropically equivalent, clarifying their classification.

Findings

Proper holomorphic polynomial maps are classified by isotropic equivalence.

Equivalence of maps is characterized by isotropic transformations.

The result applies specifically to maps preserving the origin in classical domains.

Abstract

We prove that two proper holomorphic polynomial maps between bounded symmetric domains of classical type which preserve the origin are equivalent if and only if they are isotropically equivalent.