BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Réamonn Ó Buachalla (Charles University\, Czech Republic) DTSTART:20210315T150000Z DTEND:20210315T160000Z DTSTAMP:20260422T180213Z UID:QGS/14 DESCRIPTION:Title: Qua ntum Root Vectors and a Dolbeault Double Complex for the A-Series Quantum Flag Manifolds\nby Réamonn Ó Buachalla (Charles University\, Czech R epublic) as part of Quantum Groups Seminar [QGS]\n\n\nAbstract\nIn the 200 0s a series of seminal papers by Heckenberger and Kolb introduced an essen tially unique covariant $q$-deformed de Rham complex for the irreducible q uantum flag manifolds. In the years since\, it has become increasingly cle ar that these differential graded algebras have a central role to play in the noncommutative geometry of Drinfeld-Jimbo quantum groups. Until now\, however\, the question of how to extend Heckenberger and Kolb's constructi on beyond the irreducible case has not been examined. Here we address this question for the $A$-series Drinfeld-Jimbo quantum groups $U_q(\\frak{sl} _{n+1})$\, and show that for precisely two reduced decompositions of the l ongest element of the Weyl group\, Lusztig's associated space of quantum r oot vectors gives a quantum tangent space for the full quantum flag manifo ld $\\mathcal{O}_q(F_{n+1})$ with associated differential graded algebra o f classical dimension. Moreover\, its restriction to the quantum Grassmann ians recovers the $q$-deformed complex of Heckenberger and Kolb\, giving a conceptual explanation for their origin. Time permitting\, we will discus s the noncommutative Kähler geometry of thesespaces and the proposed exte nsion of the root space construction to the other series. (Joint work with P. Somberg)\n LOCATION:https://researchseminars.org/talk/QGS/14/ END:VEVENT END:VCALENDAR