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Let $F$ be a $p$-adic field, and $K$ a quadratic extension of $F$. UsingTadic's classification of the unitary dual of $GL(n,K)$, we give the list ofirreducible unitary representations of this group distinguished by $GL(n,F)$,in terms of distinguished discrete series. As it is known that a generalisedSteinberg representation $St(k,\rho)$ is distinguished if and only if thecuspidal representation $\rho$ is $\eta^{k-1}$-distinguished, for $\eta$ thecharacter of $F^*$ with kernel the norms of $K^*$, this actually gives aclassification of distinguished unitary representations in terms ofdistinguished cuspidal representations.

Unitary representations of GL(n,K) distinguished by a Galois involution, for K a p-adic field