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- W2904111144 abstract "Let $F$ be a local non-archimedean field and $mathcal{O}_F$ its ring of integers. Let $Omega$ be a Bernstein component of the category of smooth representations of $GL_n(F)$, let $(J, lambda)$ be a Bushnell-Kutzko $Omega$-type, and let $mathfrak{Z}_{Omega}$ be the centre of the Bernstein component $Omega$. This paper contains two major results. Let $sigma$ be a direct summand of $mathrm{Ind}_J^{GL_n(mathcal{O}_F)} lambda$. We will begin by computing $mathrm{ctext{--} Ind}_{GL_n(mathcal{O}_F)}^{GL_n(F)} sigmaotimes_{mathfrak{Z}_{Omega}}kappa(mathfrak{m})$, where $kappa(mathfrak{m})$ is the residue field at maximal ideal $mathfrak{m}$ of $mathfrak{Z}_{Omega}$, and the maximal ideal $mathfrak{m}$ belongs to a Zariski-dense set in $mathrm{Spec}: mathfrak{Z}_{Omega}$. This result allows us to deduce that the endomorphism ring $mathrm{End}_{GL_n(F)}(mathrm{ctext{--} Ind}_{GL_n(mathcal{O}_F)}^{GL_n(F)} sigma)$ is isomorphic to $mathfrak{Z}_{Omega}$, when $sigma$ appears with multiplicity one in $mathrm{Ind}_J^{GL_n(mathcal{O}_F)} lambda$." @default.
- W2904111144 created "2018-12-22" @default.
- W2904111144 creator A5050964466 @default.
- W2904111144 date "2018-03-05" @default.
- W2904111144 modified "2023-09-27" @default.
- W2904111144 title "The endomorphism ring of projectives and the Bernstein centre" @default.
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