Higher level cusp forms on the exceptional group of type E₇

2017/11/10 by Henry H. Kim, Kim, Henry H., Takuya Yamauchi +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1711.03785

openalex publication_date 2017/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By using new techniques with the degenerate Whittaker functions found by Ikeda-Yamana, we construct higher level cusp form on E_7,3, called Ikeda type lift, from any Hecke cusp form whose corresponding automorphic representation has no supercuspidal local components. This generalizes the previous results on level one forms. But there are new phenomena in higher levels; first, we can handle non-trivial central characters. Second, the lift depends only on the restriction of the Hecke cusp form to SL₂. Hence any twist of the cusp form gives rise to the same lift. However for square free levels with the trivial central character, there is no such ambiguity.

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