Geodesic
Quaternionic Speh representations
Documenta mathematica, Tome 28 (2023) no. 4, pp. 903-937

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For a central division algebra D, we study a family of representations of GLk,D​ (both locally and globally), which can be viewed as analogs of the Speh representations. At the non- Archimedean places, we show that these representations support unique models of degenerate type. Globally, we show that these representations support certain non-vanishing Fourier coefficients. We also obtain some partial results regarding unique models at the Archimedean places.
DOI : 10.4171/dm/928
Classification : 11F70, 22E50, 22E55
Mots-clés : Generalized Whittaker coefficients, Jacquet–Langlands correspondence, Speh representations, unique models 
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     author = {Yuanqing Cai},
     title = {Quaternionic {Speh} representations},
     journal = {Documenta mathematica},
     pages = {903--937},
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     volume = {28},
     number = {4},
     year = {2023},
     doi = {10.4171/dm/928},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/928/}
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Yuanqing Cai. Quaternionic Speh representations. Documenta mathematica, Tome 28 (2023) no. 4, pp. 903-937. doi: 10.4171/dm/928

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