Langlands functoriality conjecture for ${\bf SO}_{2n}^*$ in positive characteristic

TL;DR

This paper proves the Langlands functoriality conjecture for certain non-split special orthogonal groups in positive characteristic, extending prior results and confirming key aspects of automorphic representation theory.

Contribution

It establishes the functoriality for quasi-split non-split even special orthogonal groups in positive characteristic, a significant extension of existing results.

Findings

Proves functoriality for non-split orthogonal groups in positive characteristic.

Confirms compatibility of local gamma factors.

Supports the unramified Ramanujan conjecture.

Abstract

In this article, we are concerned with the Langlands functoriality conjecture. Cogdell, Kim, Piatetski-Shapiro and Shahidi proved functioriality conjecture in the case of a globally generic cuspidal automorphic representation for the split classical groups, unitary groups or even quasi-split special orthogonal groups in characteristic zero. Lomel\'i extends this result to split classical groups and unitary groups in positive characteristic. Thus, in this article we prove the Langlands functoriality conjecture for the even quasi-split non-split special orthogonal groups in positive characteristic i.e. we lift globally generic cuspidal automorphic representations of quasi-split non-split even special orthogonal groups to generic automorphic representations of suitable general linear groups in positive characteristic. As an application of this result, we prove the compatibility of the local gamma factors and the unramified Ramanujan conjecture.