BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Pavel Turek (Royal Holloway\, University of London) DTSTART:20230124T073000Z DTEND:20230124T083000Z DTSTAMP:20260423T021218Z UID:OISTRTS/45 DESCRIPTION:Title: On stable modular plethysms of the natural module of $\\textrm{SL}_2(\\ma thbb{F}_p)$ in characteristic $p$\nby Pavel Turek (Royal Holloway\, Un iversity of London) as part of OIST representation theory seminar\n\n\nAbs tract\nTo study polynomial representations of general and special linear g roups in characteristic zero one can use formal characters to work with sy mmetric functions instead. The situation gets more complicated when workin g over a field $k$ of non-zero characteristic. However\, by describing the representation ring of $k\\textrm{SL}_2(\\mathbb{F}_p)$ modulo projective modules appropriately we are able to use symmetric functions with a suita ble specialisation to study a family of polynomial representations of $k\\ textrm{SL}_2(\\mathbb{F}_p)$ in the stable category. In this talk we descr ibe how this introduction of symmetric functions works and how to compute various modular plethysms of the natural $k\\textrm{SL}_2(\\mathbb{F}_p)$- module in the stable category. As an application we classify which of thes e modular plethysms are projective and which are `close' to being projecti ve. If time permits\, we describe how to generalise these classifications using a rule for exchanging Schur functors and tensoring with an endotrivi al module.\n LOCATION:https://researchseminars.org/talk/OISTRTS/45/ END:VEVENT END:VCALENDAR