BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Maarten Solleveld (Radboud Universiteit) DTSTART:20210202T160000Z DTEND:20210202T170000Z DTSTAMP:20260423T004143Z UID:GNTRT/2 DESCRIPTION:Title: Be rnstein Components and Hecke Algebras for $p$-adic Groups\nby Maarten Solleveld (Radboud Universiteit) as part of Geometry\, Number Theory and R epresentation Theory Seminar\n\n\nAbstract\nSuppose that one has a supercu spidal representation of a Levi subgroup of some reductive \n$p$-adic grou p $G$. Bernstein associated to this a block $\\mathrm{Rep}(G)^s$ in the ca tegory of smooth $G$-representations. We address the question: what does $ \\mathrm{Rep}(G)^s$ look like? Usually this is investigated with Bushnell- -Kutzko types\, but these are not always available. Instead\, we approach it via a progenerator of $\\mathrm{Rep}(G)^s.$ We will discuss the structu re of the $G$\n-endomorphism algebra of such a progenerator in detail. We will show that $\\mathrm{Rep}(G)^s$\nis "almost" equivalent with the modul e category of an affine Hecke algebra -- a statement that will be made pre cise in several ways. In the end\, this leads to a classification of the i rreducible representations in $\\mathrm{Rep}(G)^s$ in terms of the complex torus and the finite group that are canonically associated to this Bernst ein component.\n LOCATION:https://researchseminars.org/talk/GNTRT/2/ END:VEVENT END:VCALENDAR