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Cocenter of p-adic groups, II: Induction map

Xuhua He

Representation Theory mathscidoc:1912.43223

Advances in Mathematics, 345, 972-997, 2019.3
In this paper, we study some relation between the cocenter H(G) of the Hecke algebra H (G) of a connected reductive group G over a nonarchimedean local field and the cocenter H(M) of its Levi subgroups M. Given any Newton component of H(G), we construct the induction map i from the corresponding Newton component of H(M) to it. We show that this map is an isomorphism. This leads to the BernsteinLusztig type presentation of the cocenter H(G), which generalizes the work [11] on the affine Hecke algebras. We also show that the map i we constructed is adjoint to the Jacquet functor.
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@inproceedings{xuhua2019cocenter,
  title={Cocenter of p-adic groups, II: Induction map},
  author={Xuhua He},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113033847005783},
  booktitle={Advances in Mathematics},
  volume={345},
  pages={972-997},
  year={2019},
}
Xuhua He. Cocenter of p-adic groups, II: Induction map. 2019. Vol. 345. In Advances in Mathematics. pp.972-997. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113033847005783.
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