Variation of Additive Characters in the Transfer for Mp(2n)

New research explores the behavior of endoscopic transfer for the metaplectic group Mp(2n) over a local field.

Mar. 20, 2026 at 12:00am

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This research note examines the behavior of endoscopic transfer for the metaplectic group Mp(2n) of rank n over a local field F of characteristic zero, focusing on the variation of additive characters in this transfer process.

Why it matters

The metaplectic group Mp(2n) is an important object of study in representation theory and automorphic forms. Understanding the endoscopic transfer for Mp(2n) and how additive characters behave in this process can provide insights into the structure and properties of this group, with potential applications in areas like the Langlands program.

The details

The author determines the behavior of endoscopic transfer for Mp(2n) under variation of additive characters. This builds on prior work on the endoscopic classification of representations for orthogonal and symplectic groups, as well as research on the Langlands-Weissman program for Brylinski-Deligne extensions and the Shimura-Waldspurger correspondence for Mp(2n).

  • The research was published on March 20, 2026.

The players

Wen-Wei

The author of the research note.

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The takeaway

This work contributes to the ongoing study of the metaplectic group Mp(2n) and its representation theory, with potential implications for the broader Langlands program and its connections to automorphic forms.