Strongly tempered hyperspherical Hamiltonian spaces

TL;DR

This paper classifies strongly tempered hyperspherical Hamiltonian spaces, revealing connections to known integrals and proposing new ones, thus deepening understanding of period integrals in representation theory.

Contribution

It provides a complete classification of strongly tempered hyperspherical Hamiltonian spaces and links their period integrals to classical and new integrals, offering new insights.

Findings

Identification of a complete list of strongly tempered hyperspherical Hamiltonian spaces

Connection of period integrals to Rankin-Selberg and other known integrals

Proposal of new interesting period integrals for further study

Abstract

In this paper, we give a complete list of strongly tempered hyperspherical Hamiltonian spaces. We show that the period integrals attached to the list contains many previously studied Rankin-Selberg integrals and period integrals, thus give a new conceptual understanding of these integrals. The list also proposes many new interesting period integrals to study.