Equivalent conditions are established for a simple supercuspidal representation of GL(n,E) to be distinguished by GL(n,F) via its maximal simple type and twisted gamma factors, with the gamma factors at 1/2 sufficient to decide distinction.
Prasad,Trilinear forms for representations ofGL(2)and localϵ-factors, Compositio Math.75 (1990), no
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Distinguished Simple Supercuspidal Representations of $p$-adic $\text{GL}(n)$
Equivalent conditions are established for a simple supercuspidal representation of GL(n,E) to be distinguished by GL(n,F) via its maximal simple type and twisted gamma factors, with the gamma factors at 1/2 sufficient to decide distinction.