Seesaw Identities and Theta Contractions with Generalized Theta Functions, and Restrictions of Theta Lifts

TL;DR

This paper develops a seesaw identity for theta functions with polynomials, derives a formula for theta contractions, and applies these results to analyze restrictions of theta lifts to sub-Grassmannians, with various applications.

Contribution

It introduces a new seesaw identity for polynomial theta functions and a formula for theta contractions, advancing the understanding of theta lift restrictions.

Findings

Established a seesaw identity for polynomial theta functions

Derived a formula for theta contractions

Applied results to restrictions of theta lifts to sub-Grassmannians

Abstract

We prove a seesaw identity for theta functions with polynomials, and establish a formula for the corresponding theta contractions. We then use it to determine the restrictions of theta lifts to sub-Grassmannians, with some applications.