Twisted doubling integrals for classical groups

TL;DR

This paper provides a conceptual framework for twisted doubling integrals for classical groups, extending the construction to quaternionic unitary groups and analyzing their properties through unfolding and degenerate Whittaker coefficients.

Contribution

It introduces a unified approach to twisted doubling integrals, extending their applicability to quaternionic unitary groups and analyzing key properties with new tools.

Findings

Unified unfolding argument for twisted doubling integrals

Extension to quaternionic unitary groups

Properties of degenerate Whittaker coefficients

Abstract

We describe the twisted doubling integrals of Cai-Friedberg-Ginzburg-Kaplan in a conceptual way. This also extends the construction to the quaternionic unitary groups. We carry out the unfolding argument uniformly in this article. To do so, we define a family of degenerate Whittaker coefficients that are suitable in this setup and study some of their properties. We also prove certain related global and local results that use the same tools.