BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Inês Rodrigues (University of Lisbon) DTSTART:20210401T185000Z DTEND:20210401T195000Z DTSTAMP:20260423T005853Z UID:GPRTatNU/26 DESCRIPTION:Title: A cactus group action on shifted tableau crystals and a shifted Berenste in-Kirillov group\nby Inês Rodrigues (University of Lisbon) as part o f Geometry\, Physics\, and Representation Theory Seminar\n\n\nAbstract\nGi llespie\, Levinson and Purbhoo introduced a crystal-like structure for shi fted tableaux\, called the shifted tableau crystal. Following a similar ap proach as Halacheva\, we exhibit a natural internal action of the cactus g roup on this structure\, realized by the restrictions of the shifted Schü tzenberger involution to all primed intervals of the underlying crystal al phabet. This includes the shifted crystal reflection operators\, which agr ee with the restrictions of the shifted Schützenberger involution to sing le-coloured connected components\, but unlike the case for type A crystals \, these do not need to satisfy the braid relations of the symmetric group .\n\nIn addition\, we define a shifted version of the Berenstein-Kirillov group\, by considering shifted Bender-Knuth involutions. Paralleling the w orks of Halacheva and Chmutov\, Glick and Pylyavskyy for type A semistanda rd tableaux of straight shape\, we exhibit another occurrence of the cactu s group action on shifted tableau crystals of straight shape via the actio n of the shifted Berenstein-Kirillov group. We conclude that the shifted B erenstein-Kirillov group is isomorphic to a quotient of the cactus group. Not all known relations that hold in the classic Berenstein-Kirillov group need to be satisfied by the shifted Bender-Knuth involutions\, namely the one equivalent to the braid relations of the type A crystal reflection op erators\, but the ones implying the relations of the cactus group are veri fied\, thus we have another presentation for the cactus group in terms of shifted Bender-Knuth involutions.\n LOCATION:https://researchseminars.org/talk/GPRTatNU/26/ END:VEVENT END:VCALENDAR