Explicit Hecke descent for special cycles

TL;DR

This paper derives an explicit formula for how geometric Hecke correspondences act on special cycles in Shimura varieties, comparing two formulas and showing they generally differ.

Contribution

It provides a new explicit formula for Hecke actions on special cycles and analyzes the differences between related existing formulas.

Findings

Derived an explicit formula for Hecke action on special cycles.

Compared two formulas and showed they do not always agree.

Provides insights into the structure of special cycles under Hecke correspondences.

Abstract

We derive an explicit formula for the action of a geometric Hecke correspondence on special cycles on a Shimura variety in terms of such cycles at a fixed neat level and compare it with another closely related expression sometimes used in literature. We provide evidence that the two formulas do not agree in general.