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Creators/Authors contains: "Takeda, Shuichiro"

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  1. ; (, Mathematische Zeitschrift)
    Each orthogonal group O(n) has a nontrivial GL(1)-extension, which we call GPin(n). The identity component of GPin(n) is the more familiar GSpin(n), the general Spin group. We prove that the restriction toGPin(n−1) of an irreducible admissible representation ofGPin(n) over a nonarchimedean local field of characteristic zero is multiplicity free and also prove the analogous theorem for GSpin(n). Our proof uses the method of Aizenbud, Gourevitch, Rallis and Schiffman, who proved the analogous theorem for O(n), and of Waldspurger, who proved that for SO(n). We also give an explicit description of the contragredient of an irreducible admissible representation of GPin(n) and GSpin(n), which is needed to apply their method to our situations. 
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