BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Max Gurevich (Technion) DTSTART:20210528T073000Z DTEND:20210528T083000Z DTSTAMP:20260423T021219Z UID:OISTRTS/17 DESCRIPTION:Title: New constructions for irreducible representations in monoidal categories of type A\nby Max Gurevich (Technion) as part of OIST representation t heory seminar\n\n\nAbstract\nOne ever-recurring goal of Lie theory is the quest for effective and elegant descriptions of collections of simple obje cts in categories of interest. A cornerstone feat achieved by Zelevinsky i n that regard\, was the combinatorial explication of the Langlands classif ication for smooth irreducible representations of p-adic GL_n. It was a fo rerunner for an exploration of similar classifications for various categor ies of similar nature\, such as modules over affine Hecke algebras or quan tum affine algebras\, to name a few. \nA next step - reaching an effective understanding of all reducible finite-length representations remains larg ely a difficult task throughout these settings.\n\nRecently\, joint with E rez Lapid\, we have revisited the original Zelevinsky setting by suggestin g a refined construction of all irreducible representations\, with the hop e of shedding light on standing decomposition problems. This construction applies the Robinson-Schensted-Knuth transform\, while categorifying the d eterminantal Doubilet-Rota-Stein basis for matrix polynomial rings appeari ng in invariant theory.\nIn this talk\, I would like to introduce the new construction into the setting of modules over quiver Hecke (KLR) algebras. In type A\, this category may be viewed as a quantization/gradation of th e category of representations of p-adic groups. I will explain how adoptin g that point of view and exploiting recent developments in the subject (su ch as the normal sequence notion of Kashiwara-Kim) brings some conjectural properties of the RSK construction (back in the p-adic setting) into reso lution.\nTime permits\, I will discuss the relevance of the RSK constructi on to the representation theory of cyclotomic Hecke algebras.\n LOCATION:https://researchseminars.org/talk/OISTRTS/17/ END:VEVENT END:VCALENDAR