Webs and Howe duality for the quantum orthogonal group

event Friday, December 6, 2024
access_time 4:00pm (CST)
room PHSC 1105
free_breakfast Tea at 3:30pm (CST) in PHSC 424

Abstract: The Jones polynomial can be defined with the Temperley-Lieb category, whose Karoubian completion is equivalent to the representation category of quantum SL(2). In order to generalize the equivalence between a graphical category and the representation category of a quantum group, G. Kuperberg introduced web categories for rank 2 Lie algebras, where trivalent graphs are used in addition to planar matchings. Web categories have been widely studied since then. I will talk about how to define the web category for the quantum orthogonal group, based on joint work with E. Bodish. I will also talk about recent progress on studying the quantum Howe duality for the orthogonal group, which has potential connections to the i-quantum group, based on upcoming joint work with E.Bodish and D.Tubbenhauer.


For more information on this event, please contact Roi Docampo.