A REMARK ON JACQUET-LANGLANDS CORRESPONDENCE AND INVARIANT s

Let F be a non-Archimedean local field, and let G be an inner form of GL(N)(F) with N >= 1. Let JL be the Jacquet Langlands correspondence between GL(N)(F) and G. In this paper, we compute the invariant s associated with the essentially square integrable representation JL(-1) (rho) for a cuspidal representation rho of G by using the recent results of Bushnell and Henniart, and we restate the second part of a theorem given by Deligne, Kazhdan, and Vigneras in terms of the invariant s. Moreover, by using the parametric degree, we present a proof of the first part of the theorem.