# Epsilon dichotomy for linear models.

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Hang Xue, The University of Arizona
Fine Hall 214

Saito--Tunnell theorem is a local version of Waldspurger's  formula, relating the existence of E^\times invariant linear forms on representation of GL_2 to local root numbers. I present a  generalization of this which relates the existence of GL_n(E) invariant linear forms on GL_2n(F) to local root numbers. The proof  relies on a "relative version" of Harish-Chandra' theory of local  character expansions.