# Definition of Base Change of representation

Recently, I read the paper on Ichino-Ikeda conjecture for unitary groups by Raphaël Beuzart-Plessis (https://arxiv.org/pdf/1602.06538.pdf). 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