BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Andrea Appel (University of Parma\, Italy) DTSTART:20210322T150000Z DTEND:20210322T160000Z DTSTAMP:20260422T182333Z UID:QGS/15 DESCRIPTION:Title: Qua ntum affine algebras and spectral k-matrices\nby Andrea Appel (Univers ity of Parma\, Italy) as part of Quantum Groups Seminar [QGS]\n\n\nAbstrac t\nThe Yang-Baxter equation (YBE) and the reflection equation (RE) are two fundamental\nsymmetries in mathematics arising from particles moving alon g a line or a half-line.\nThe quest for constant solutions of YBE (R-matri ces) is at the very origin of the Drinfeld-Jimbo\nquantum groups and their universal R-matrix. Similarly\, constant solutions of RE (k-matrices)\nna turally appear in the context of quantum symmetric pairs (QSP).\n\nIn join t work with Bart Vlaar\, we construct a discrete family of universal k-mat rices associated to\nan arbitrary quantum symmetric Kac-Moody pair as oper ators on category O integrable\nrepresentations. This generalises previous results by Balagovic-Kolb and Bao-Wang valid\nfor finite-type QSP. In thi s talk\, I will explain how\, in affine type\, this construction gives ris e to\nparameter-dependent operators (spectral k-matrices) on finite-dimens ional representations of\nquantum loop algebras solving the same RE introd uced by Cherednik and Sklyanin in the 1980s\nin the context of quantum int egrability near a boundary.\n LOCATION:https://researchseminars.org/talk/QGS/15/ END:VEVENT END:VCALENDAR