On the stable transfer for $\textrm{Sym}^n$ lifting of $\textrm{GL}_2$: Archimedean case

Abstract: Following the paradigm of R. Langlands, we are going to explore the the stable transfer factors for $\textnormal{Sym}^{n}$ lifting from $\textnormal{GL}_{2}$ to $\textnormal{GL}_{n+1}$. We give a complete answer for tempered principal series over any local fields of characteristic zero, which in particular resolve the case over complex field. Over real field, when $n$ is odd, we provide a reduction formula, reducing the construction of the stable transfer factors to diagonal embedding of $\textnormal{GL}_{2}$ to finitely many copies of $\textnormal{GL}_{2}$. There are also partial results over $p$-adic fields.

This is a joint work with D. Johnstone. Preprint available arXiv:2002.09551.

number theoryrepresentation theory

Audience: researchers in the topic

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