Bernstein Centre

Alexandre Pyvovarov
2019-12-26 10:30-11:30

Speaker: Dr. Alexandre Pyvovarov (MCM)
Title: Bernstein Centre
Time: 10:30-11:30am, Dec 26, 2019
Place: MCM110
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 $\Omega$. We will explain how to compute $(\mathrm{c\text{--} Ind}_{GL_n(\mathcal{O}_F)}^{GL_n(F)} \lambda)\otimes_{\mathfrak{Z}_{\Omega}}\kappa(\mathfrak{m})$, 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 $\mathrm{Spec}\: \mathfrak{Z}_{\Omega}$.