Distinguished representations for $SL(2)$

Let $E/F$ be a quadratic extension of $p$-adic fields. We compute the multiplicity of the space of $SL_2(F)$-invariant linear forms on a representation of $SL_2(E)$. This multiplicity varies inside an $L$-packet similar in spirit to the multiplicity formula for automorphic representations due to Labesse and Langlands.

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Published 1 January 2003