Mathematical Research Letters
Volume 10 (2003)
Distinguished representations for $SL(2)$
Pages: 867 – 878
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.