2020/02/21 by Daniel Johnstone, Johnstone, Daniel, Zhilin Luo +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Combinatorics #Computer science #Diagonal #Embedding #FOS: Mathematics #Field (mathematics) #Finite Group Theory Research #Geometry #Mathematics #Morphism #Number Theory (math.NT) #Philosophy #Physics #Pure mathematics #Representation Theory (math.RT) #Residue (chemistry) #Residue field #Transfer (computing) #Zero (linguistics) #math.NT #math.RT
paper · pdf · doi:10.48550/arxiv.2002.09551
Comments are welcome
arxiv created 2020/02/21 · openalex publication_date 2020/02/21 · arxiv updated 2020/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Following the paradigm of \citeMR3117742, we are going to explore the stable transfer factors for Symn lifting from GL2 to GLn+1 over any local fields F of characteristic zero with residue characteristic not equal to 2. When F=ℂ we construct an explicit stable transfer factor for any n. When n is odd, we provide a reduction formula, reducing the question to the construction of the stable transfer factors when the L-morphism is the diagonal embedding from GL2(ℂ) to finitely many copies of GL2(ℂ) under mild assumptions on the residue characteristic of F. With the assumptions on the residue characteristic, the reduction formula works uniformly over any local fields of characteristic zero, except that for p-adic situation we need to exclude the twisted Steinberg representations.