Model transition under local theta correspondence

TL;DR

This paper investigates how models of representations change within the local theta correspondence between split even special orthogonal and symplectic groups over non-archimedean fields, focusing on representation transitions.

Contribution

It provides new insights into the behavior of models during the local theta correspondence for specific classical groups over non-archimedean fields.

Findings

Characterizes model transitions in the local theta correspondence.

Identifies conditions for model stability during the transfer.

Enhances understanding of representation theory for classical groups.

Abstract

We study model transition for representations occurring in the local theta correspondence between split even special orthogonal groups and symplectic groups, over a non-archimedean local field of characteristic zero.