Quasi-pullback of Borcherds products

TL;DR

This paper develops an explicit formula for the quasi-pullback operation of Borcherds products, enabling the construction of lower-dimensional Borcherds products via a renormalized restriction process.

Contribution

It provides a new explicit formula for the weakly holomorphic modular form whose Borcherds lift corresponds to the quasi-pullback of a given Borcherds product.

Findings

Explicit formula for the weakly holomorphic modular form of Weil representation type.

Demonstration that quasi-pullback produces a Borcherds product on a lower-dimensional domain.

Enhanced understanding of the structure of Borcherds products under restriction operations.

Abstract

Quasi-pullback of Borcherds products is an operation of renormalized restriction. It produces a meromorphic modular form on a lower dimensional symmetric domain which is again a Borcherds product. We give an explicit formula for the weakly holomorphic modular form of Weil representation type whose Borcherds lift is the quasi-pullback of the given Borcherds product.