The Local Ginzburg-Rallis Model Over Complex Field

TL;DR

This paper investigates the local Ginzburg-Rallis model over complex fields, establishing that the multiplicity is generally one for most generic representations, and provides partial results for the real case.

Contribution

It extends previous work by analyzing the complex case and offers new results on multiplicity one for generic representations in this setting.

Findings

Multiplicity is always 1 for most generic representations over complex fields

Partial results obtained for the real case for general generic representations

Builds on prior work for p-adic and tempered representations

Abstract

We consider the local Ginzburg-Rallis model over complex field. We show that the multiplicity is always 1 for a majority of the generic representations. We also have partial results on the real case for general generic representations. This is a sequel work of [Wan15] and [Wan16] on which we considered the p-adic case and the real case for tempered representations.