BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Pavel Turek (OIST) DTSTART:20260120T060000Z DTEND:20260120T070000Z DTSTAMP:20260423T021308Z UID:OISTRTS/77 DESCRIPTION:Title: Balanced columns of decomposition matrices\nby Pavel Turek (OIST) as part of OIST representation theory seminar\n\n\nAbstract\nThe decompositio n matrices describe how the irreducible modules of symmetric groups in cha racteristic zero decompose in prime characteristic. Understanding these ma trices\, and in particular\, finding a combinatorial description of their entries\, is a central open problem in the representation theory of symmet ric groups. The main result of the talk is a description of columns of the se matrices indexed by ‘d-balanced’ partitions for d=2. It is a conseq uence of a more general result which describes these columns for any d>1 u nder some additional assumptions. As a further result\, we show that there are many 2-balanced partitions. The key players in the proof of the prese nted results are Foulkes modules\, which are used to construct certain pro jective modules\, and the Jantzen-Schaper formula\, which allows us to tra nsfer the algebraic problem into a combinatorial system of equalities\, wh ich can then be solved using a new algorithm defined on Young diagrams. Th is is joint work with Bim Gustavsson\, David Hemmer and Stacey Law.\n LOCATION:https://researchseminars.org/talk/OISTRTS/77/ END:VEVENT END:VCALENDAR