# Local newforms for the general linear groups over a non-archimedean local field

@inproceedings{Atobe2021LocalNF, title={Local newforms for the general linear groups over a non-archimedean local field}, author={Hiraku Atobe and Satoshi Kondo and Seidai Yasuda}, year={2021} }

In [12], Jacquet–Piatetskii-Shapiro–Shalika defined a family of compact open subgroups of p-adic general linear groups indexed by non-negative 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 non-negative integers. For the proof, we introduce the Rankin–Selberg integrals for Speh…

## One Citation

On branching laws of Speh representations

- Mathematics
- 2021

In this paper, we consider the branching law of the Speh representation Sp(π, n+ l) of GL2n+2l with respect to the block diagonal subgroup GLn ×GLn+2l for any irreducible generic representation π of…

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