BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Réamonn Ó Buachalla (Charles University\, Prague) DTSTART:20211208T200000Z DTEND:20211208T210000Z DTSTAMP:20260420T052739Z UID:NYC-NCG/82 DESCRIPTION:Title: Quantum Root Vectors and a Dolbeault Double Complex for the A-Series Quan tum Flag Manifolds\nby Réamonn Ó Buachalla (Charles University\, Pra gue) as part of Noncommutative geometry in NYC\n\n\nAbstract\nIn the 2000s a series of seminal papers by Heckenberger and Kolb introduced an essenti ally unique covariant $q$-deformed de Rham complex for the irreducible qua ntum flag manifolds. In the years since\, it has become increasingly clear that these differential graded algebras have a central role to play in th e noncommutative geometry of Drinfeld–Jimbo quantum groups. Until now\, however\, the question of how to extend Heckenberger and Kolb’s construc tion beyond the irreducible case has not been examined. Here we address th is question for the A-series Drinfeld–Jimbo quantum groups $U_q(\\mathfr ak{sl}_{n+1})$\, and show that for precisely two reduced decompositions of the longest element of the Weyl group\, Lusztig’s associated space of q uantum root vectors gives a quantum tangent space for the full quantum fla g manifold $\\mathcal{O}_q(F_{n+1})$ with associated differential graded a lgebra of classical dimension. Moreover\, its restriction to the quantum G rassmannians recovers the $q$-deformed complex of Heckenberger and Kolb\, giving a conceptual explanation for their origin. Time permitting\, we wil l discuss the noncommutative Kähler geometry of these spaces and the prop osed extension of the root space construction to the other series. (Joint work with P. Somberg.)\n LOCATION:https://researchseminars.org/talk/NYC-NCG/82/ END:VEVENT END:VCALENDAR