Abstract
In this paper we prove a division algebra analogue of a theorem of Jacquet and Rallis about uniqueness ofGLn(k)×GLn(k) invariant linear form on an irreducible admissible representation ofGL2n(k). We propose a conjecture about when this invariant form exists. We prove some results about self-dual representations of the invertible elements of a division algebra and of Galois groups of local fields. The Shalika model has been studied for principal series representations ofGL2(D) forDa division algebra and a conjecture made regarding its existence in general.
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