Recently, I read the paper on Ichino-Ikeda conjecture for unitary groups by Raphaël Beuzart-Plessis ( In the introduction, it says that

Let $BC(\Pi)$ be the base change of $\Pi$ to $GL_n(\mathbb{A}_E)\times GL_{n+1}(\mathbb{A}_E)$ (known to exist thanks to the recent work of Mok and Kaletha, Minguez, Shin and White).

where $\Pi$ is a cuspidal automorphic representation of $U(n)\times U(n+1)(\mathbb{A}_F)$. $E$ and $F$ are number field, and $E$ is a quadratic extension of $F$.

I am a bit confused about the conception of base change. It seems that it is a general conception. Thank you if you can tell me the general definition of the base change of automorphic representation using the representation language.

  • Do you know what it is for a single unitary group? On the product it will just be the product. What it conjecturally is is explained in many expositions of automorphic representations, e.g., Arthur-Gelbart. – Kimball Sep 12 at 23:06

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.