Symplectic duality between complex domains

TL;DR

This paper extends the concept of symplectic duality from bounded symmetric domains to all complex domains in orm, generalizing previous results and broadening the scope of the theory.

Contribution

It generalizes the definition of symplectic duality to arbitrary complex domains and extends prior results from symmetric domains to these more general settings.

Findings

Extended symplectic duality to all complex domains in orm.

Generalized previous results to broader classes of domains.

Provided new insights into the structure of complex domains.

Abstract

In this paper after extending the definition of symplectic duality (given by the first two authors in arXiv:math/0603141 for bounded symmetric domains) to arbitrary complex domains of ${\C}^n$ centered at the origin we generalize some of the results proved in arXiv:math/0603141 and arXiv:0707.2125 to those domains.