Mathematical Research Letters

Volume 10 (2003)

Number 6

Distinguished representations for $SL(2)$

Pages: 867 – 878

DOI: http://dx.doi.org/10.4310/MRL.2003.v10.n6.a12

Authors

U. K. Anandavardhanan

Dipendra Prasad

Abstract

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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