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      Distinguished Representations for SLn(D) where D is a quaternion division algebra over a p-adic field

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          Abstract

          Let D be a quaternion division algebra over a non-archimedean local field F of characteristic zero. Let E/F be a quadratic extension and SLn(E)=GLn(E)SLn(D). We study distinguished representations of SLn(D) by the subgroup SLn(E). Let π be an irreducible admissible representation of SLn(D) which is distinguished by SLn(E). We give a multiplicity formula, i.e. a formula for the dimension of the C-vector space HomSLn(E)(π,\mathbbm1), where \mathbbm1 denotes the trivial representation of SLn(E). This work is a non-split inner form analog of a work by Anandavardhanan-Prasad which gives a multiplicity formula for SLn(F)-distinguished irreducible admissible representation of SLn(E).

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          Journal
          08 January 2025
          Article
          2501.04500
          399cbfb4-87c1-4d07-8049-cc4bc1ccaf32

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          22E50, 11S37, 20G25, 22E35
          math.RT math.NT

          Number theory,Algebra
          Number theory, Algebra

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