Lifting orthogonal representations to spin groups and local root numbers

Dipendra Prasad and Dinakar Ramakrishnan

MSRI #1995-018

Representations of $D_k^*/k^*$ for a quaternion
division algebra $D_k$ over a local field $k$ are orthogonal
representations. In this note we  
investigate when these orthogonal representations can be lifted to the
corresponding spin group. The results are expressed in terms of local root
number of the representation.