Big Theta equals small theta generically

TL;DR

This paper investigates the theta correspondence over non-Archimedean local fields, demonstrating that under certain conditions, the big theta lift is irreducible using homological methods and derivatives.

Contribution

It introduces a new approach combining homological methods and derivatives to establish irreducibility of big theta lifts under mild conditions.

Findings

Big theta lift is irreducible under mild conditions

Homological methods are effective in analyzing theta correspondence

Provides new insights into the structure of theta lifts

Abstract

In this paper we consider the theta correspondence over a non-Archimedean local field. Using the homological method and the theory of derivatives, we show that under a mild condition the big theta lift is irreducible.