# Generic representations of metaplectic groups and their theta lifts

## TL;DR

This paper characterizes generic representations of metaplectic groups over p-adic fields via Langlands parameters and computes their theta lifts across all levels for odd orthogonal group towers, also analyzing the failure of the standard module conjecture.

## Contribution

It provides a comprehensive description of generic representations and their theta lifts for metaplectic groups, including the detailed analysis of the standard module conjecture failure.

## Key findings

- Explicit description of generic representations via Langlands parameters
- Calculation of theta lifts for all levels in odd orthogonal towers
- Identification of cases where the standard module conjecture fails

## Abstract

In this paper we give the description of generic representations of metaplectic groups over p-adic fields in terms of their Langlands parameters and calculate their theta lifts on all levels for any tower of odd orthogonal groups. We also describe precisely all the occurrences of the failure of the standard module conjecture for metaplectic groups.