BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Chris Chung (Okinawa Institute of Science and Technology) DTSTART:20210126T073000Z DTEND:20210126T083000Z DTSTAMP:20260423T021307Z UID:OISTRTS/9 DESCRIPTION:Title: \\(\\imath\\)Quantum Covering Groups: Serre presentation and canonical bas is\nby Chris Chung (Okinawa Institute of Science and Technology) as pa rt of OIST representation theory seminar\n\n\nAbstract\nIn 2016\, Bao and Wang developed a general theory of canonical basis for quantum symmetric p airs \\((\\mathbf{U}\, \\mathbf{U}^\\imath)\\)\, generalizing the canonica l basis of Lusztig and Kashiwara for quantum groups and earning them the 2 020 Chevalley Prize in Lie Theory. The \\(\\imath\\)divided powers are pol ynomials in a single generator that generalize Lusztig's divided powers\, which are monomials. They can be similarly perceived as canonical basis in rank one\, and have closed form expansion formulas\, established by Berma n and Wang\, that were used by Chen\, Lu and Wang to give a Serre presenta tion for coideal subalgebras \\(\\mathbf{U}^\\imath\\)\, featuring novel \ \(\\imath\\)Serre relations when \\(\\tau(i) = i\\).\n\nQuantum covering g roups\, developed by Clark\, Hill and Wang\, are a generalization that `co vers' both the Lusztig quantum group and quantum supergroups of anisotropi c type. In this talk\, I will talk about how the results for \\(\\imath\\) -divided powers and the Serre presentation can be extended to the quantum covering algebra setting\, and subsequently applications to canonical basi s for \\(\\mathbf{U}^\\imath_\\pi\\)\, the quantum covering analogue of \\ (\\mathbf{U}^\\imath\\)\, and quantum covering groups at roots of 1.\n LOCATION:https://researchseminars.org/talk/OISTRTS/9/ END:VEVENT END:VCALENDAR