LIFTING ORTHOGONAL REPRESENTATIONS TO

SPIN GROUPS AND LOCAL ROOT NUMBERS

Dipendra Prasad and Dinakar Ramakrishnan

Abstract. 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.

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