Représentations lisses de GL(m, D) II : β-extensions

Vincent Sécherre

doi:10.1112/S0010437X05001429

Abstract

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This work is concerned with type theory for reductive groups over a non Archimedean field. Given such a field F, and a division algebra D of finite dimension over its center F, we obtain results concerning the construction of simple types for the group GL(m, D), $m\geqslant1$. More precisely, for each simple stratum of the matrix algebra M(m, D), we produce a set of β-extensions in the sense of Bushnell and Kutzko.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Grabitz, Martin 2007. Simple characters for principal orders in Mm(D). Journal of Number Theory, Vol. 126, Issue. 1, p. 1.

Stevens, Shaun 2008. The supercuspidal representations of p-adic classical groups. Inventiones mathematicae, Vol. 172, Issue. 2, p. 289.

Sécherre, Vincent 2009. Proof of the Tadić conjecture (U0) on the unitary dual of GL m (D). Journal für die reine und angewandte Mathematik (Crelles Journal), Vol. 2009, Issue. 626,

Goldberg, D. Kutzko, P. and Stevens, S. 2010. Covers for Self-dual Supercuspidal Representations of the Siegel Levi Subgroup of Classical p-adic Groups. International Mathematics Research Notices,

Bushnell, Colin J. and Henniart, Guy 2011. Explicit functorial correspondences for level zero representations of p-adic linear groups. Journal of Number Theory, Vol. 131, Issue. 2, p. 309.

Sécherre, Vincent and Stevens, Shaun 2012. Smooth Representations of GLm(D) VI: Semisimple Types. International Mathematics Research Notices, Vol. 2012, Issue. 13, p. 2994.

Kariyama, Kazutoshi 2013. The formal degree of the discrete series representations ofGLm(D). Journal of Number Theory, Vol. 133, Issue. 10, p. 3426.

Bushnell, Colin J. and Henniart, Guy 2013. Intertwining of Simple Characters in GL(n). International Mathematics Research Notices, Vol. 2013, Issue. 17, p. 3977.

Mínguez, Alberto Sécherre, Vincent and Stevens, Shaun 2014. Types modulo ℓ pour les formes intérieures de GLnsur un corps local non archimédien. Proceedings of the London Mathematical Society, Vol. 109, Issue. 4, p. 823.

Bushnell, Colin J. and Henniart, Guy 2014. Modular Local Langlands Correspondence for GLn. International Mathematics Research Notices, Vol. 2014, Issue. 15, p. 4124.

Tadić, Marko 2014. Irreducibility criterion for representations induced by essentially unitary ones (case of non-archimedean GL(n,𝒜)). Glasnik Matematicki, Vol. 49, Issue. 1, p. 123.

Lapid, Erez and Mínguez, Alberto 2016. On parabolic induction on inner forms of the general linear group over a non-archimedean local field. Selecta Mathematica, Vol. 22, Issue. 4, p. 2347.

Kariyama, Kazutoshi 2017. A remark on Jacquet-Langlands correspondence and invariant $s$. Tohoku Mathematical Journal, Vol. 69, Issue. 1,

Chinello, Gianmarco 2018. Blocks of the category of smooth ℓ-modular representations of GL(n,F) and its inner forms : reduction to level 0. Algebra & Number Theory, Vol. 12, Issue. 7, p. 1675.

Lapid, Erez and Mínguez, Alberto 2018. Geometric conditions for □-irreducibility of certain representations of the general linear group over a non-archimedean local field. Advances in Mathematics, Vol. 339, Issue. , p. 113.

Imai, Naoki and Tsushima, Takahiro 2018. Local Jacquet–Langlands correspondences for simple supercuspidal representations. Kyoto Journal of Mathematics, Vol. 58, Issue. 3,

Finis, Tobias and Lapid, Erez 2019. On the analytic properties of intertwining operators II: Local degree bounds and limit multiplicities. Israel Journal of Mathematics, Vol. 230, Issue. 2, p. 771.

Bushnell, Colin J. 2019. Representations of Reductive p-adic Groups. Vol. 328, Issue. , p. 39.

KARIYAMA, Kazutoshi 2019. Classification of Very Cuspidal Representations of $\mathrm{GL}_m(D)$. Tokyo Journal of Mathematics, Vol. 42, Issue. 1,

Sécherre, Vincent and Stevens, Shaun 2019. Towards an explicit local Jacquet–Langlands correspondence beyond the cuspidal case. Compositio Mathematica, Vol. 155, Issue. 10, p. 1853.

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Représentations lisses de GL(m, D) II : β-extensions

Abstract

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This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

Représentations lisses de GL(m, D) II : β-extensions

Abstract

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