Epsilon dichotomy for twisted linear models

Abstract

Let $E/F$ be a quadratic extension of local nonarchimedean fields of characteristic zero and let $D$ be a quaternion algebra over $F$ containing $E$. In this paper, we study a relation between the existence of twisted linear models on ${\mathrm{GL}}_n(D)$ and the local root numbers.

39 pages, final version, to appear in Pacific Journal of Mathematics