Galois representations associated with unitary groups over $\mathbb Q$

Abstract

We show that a cuspidal automorphic representation $\pi ={\otimes }_{\ell \le \infty }{\pi }_{\ell }$ of a unitary similitude group $GU{\left(a,b\right)}_{∕\mathbb{Q}}$ with archimedean component ${\pi }_{\infty }$ in a regular discrete series has an associated $\left(a+b\right)$-dimensional $p$-adic Galois representation with Frobenius eigenvalues given by the local base change parameters for all primes $\ell$ such that ${\pi }_{\ell }$ and $GU\left(a,b\right)$ are unramified.