Abstract

In this talk we report on some work in progress together with Sug Woo Shin, on the construction of Galois representations for certain forms of the group \(GSO_{2n}\) over a totally real number field \(F\). More precisely, we consider a quasi-split form \(G\) of \(GSO_{2n}\)that is split if n is even and non-split if n is odd. Then we construct, for cohomological, cuspidal automorphic representations \(\pi\) of \(G\), a corresponding Galois representation, in case pi is at a finite place isomorphic (up to twist) to the Steinberg representation.