Explicit Construction of Local Langlangds Correspondence of GL(2,F) Using Theta Correspondence

2015/11/10 by Ran Cui, Cui, Ran
Mathematics · #11F27 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:11F27

paper · pdf · doi:10.48550/arxiv.1511.03309

This work was completed in 2013

arxiv created 2015/11/12 · arxiv updated 2015/11/13

Abstract

The Langlands correspondence of GL(2,F) over a non-Archimedean local field F of characteristic 0 has been well studied. The construction uses the theta correspondence. In this paper, we are going to describe explicitly how this construction is done. We will then provide new proofs to several properties of the correspondence. Including that the correspondence does not depend on the additive character introduced by the Weil representation.

Related

• On the local Langlands correspondence
• The local Langlands correspondence for GL(n) over p-adic fields
• The local Langlands correspondence for GSp₄ over local function fields
• An Approach to the Characterization of the Local Langlands Correspondence
• Geometric tamely ramified local theta correspondence in the framework of the geometric Langlands program