Explicit formulas for Hecke operators and Rankin's lemma in higher genus

TL;DR

This paper derives explicit formulas for higher genus Hecke operators, proves Rankin's lemma in genus two, and applies these results to automorphic form liftings using Ikeda-Miyawaki constructions.

Contribution

It provides explicit formulas for higher genus Hecke operators and extends Rankin's lemma to genus two, enabling new applications in automorphic form theory.

Findings

Explicit formulas for higher genus Hecke operators

Proof of Rankin's lemma in genus two

Application to automorphic form lifting

Abstract

We develop explicit formulas for Hecke operators of higher genus in terms of spherical coordinates. Applications are given to summation of various generating series with coefficients in local Hecke algebra and in a tensor product of such algebras. In particular, we formulate and prove Rankin's lemma in genus two. An application to a lifting from (GSp2 \times GSp2) to GSp4 is given using Ikeda-Miyawaki constructions.