Computing Hecke operators for arithmetic subgroups of $\text{Sp}_4$

TL;DR

This paper presents an algorithm to compute Hecke operators on equivariant cohomology for the symplectic group Sp_4, introducing a new acyclic cell complex and utilizing the well-tempered complex.

Contribution

It introduces a novel acyclic cell complex for Sp_4 and an algorithm for computing Hecke operators on equivariant cohomology.

Findings

Successful implementation of the algorithm

Construction of a new acyclic cell complex for Sp_4

Application of the well-tempered complex

Abstract

We outline an algorithm for computing Hecke operators on equivariant cohomology $H^\ast_{\Gamma_{\text{Sp}}}(X_{\text{Sp}};\rho)$ for the symplectic group $\text{Sp}_4(\mathbb{R})$. To do this, we define a new acyclic cell complex for $\text{Sp}_4(\mathbb{R})$ and make use of the well-tempered complex.