On local representation densities of hermitian forms and special cycles II

TL;DR

This paper establishes relations among representation densities of hermitian forms, introduces an efficient computational method, and applies it to compute intersection numbers of special cycles on unitary Shimura varieties, proposing a related conjecture.

Contribution

It provides new relations among representation densities and a computational approach, advancing the understanding of special cycles on unitary Shimura varieties.

Findings

Derived relations among representation densities.

Developed an efficient computation method.

Computed intersection numbers and proposed a conjecture.

Abstract

In this paper, we prove that there are certain relations among representation densities and provide an efficient way to compute representation densities by using these relations. As an application, we compute some arithmetic intersection numbers of special cycles on unitary Shimura varieties and propose a conjecture on these.