Local newforms for generic representations of unramified even unitary groups I: Even conductor case

TL;DR

This paper develops a theory of local newforms for irreducible tempered generic representations of unramified even unitary groups, utilizing advanced tools like the Gan-Gross-Prasad conjecture and theta correspondence.

Contribution

It introduces compact open subgroups for these groups and establishes the local newform theory specifically for even conductor cases, advancing the understanding of representation theory in this context.

Findings

Defined compact open subgroups for unramified even unitary groups

Established local newform theory for representations with even conductor

Connected newforms with local Gan-Gross-Prasad and theta correspondence

Abstract

In this paper, we define compact open subgroups of quasi-split even unitary groups for each even non-negative integers, and establish the theory of local newforms for irreducible tempered generic representations with a certain condition on the central characters. To do this, we use the local Gan-Gross-Prasad conjecture, the local Rankin-Selberg integrals, and the local theta correspondence.