Geodesic
Local newforms for the general linear groups over a non-archimedean local field
Forum of Mathematics, Pi, Tome 10 (2022)

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In [14], Jacquet–Piatetskii-Shapiro–Shalika defined a family of compact open subgroups of p-adic general linear groups indexed by nonnegative integers and established the theory of local newforms for irreducible generic representations. In this paper, we extend their results to all irreducible representations. To do this, we define a new family of compact open subgroups indexed by certain tuples of nonnegative integers. For the proof, we introduce the Rankin–Selberg integrals for Speh representations. 
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Hiraku Atobe; Satoshi Kondo; Seidai Yasuda. Local newforms for the general linear groups over a non-archimedean local field. Forum of Mathematics, Pi, Tome 10 (2022). doi: 10.1017/fmp.2022.17

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