BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Francesca Paganelli (U. Paris Cité) DTSTART:20261019T120000Z DTEND:20261019T130000Z DTSTAMP:20261114T040857Z UID:paris-algebra-seminar/236 DESCRIPTION:Title: Braid group invariance of quantum tori and applications\nby Francesca Paganelli (U. Paris Cité) as part of Paris algebra semina r\n\n\nAbstract\nA well-known fact in classical Lie theory is that the Wey l group W associated with a simple\, complex\, finite-dimensional Lie alge bra g acts by isometries on the dual of the Cartan subalgebra. In particul ar\, the symmetric bilinear form defined on the weight lattice is invarian t under the W-action.\n\nIn this talk\, I will present an analogue of this invariance phenomenon for skew-symmetric bicharacters in the context of q uantum affine algebras. Specifically\, we will consider the groups of fund amental and pre-fundamental l-weights (which can be viewed as affine analo gues of the fundamental weights of g). By results of Chari and Frenkel–H ernandez\, the braid group B associated with g acts on these groups of l-w eights. We then introduce the skew-symmetric bicharacters on the groups of l-weights defined by Nakajima and Hernandez\, and extended by Bittmann an d myself. I will show that these bicharacters are invariant under the B-ac tion on l-weight groups\, and present an application concerning quantum QQ -systems in the theory of shifted quantum groups.\n\nThis talk will take p lace in hybrid mode at the Institut Henri Poincaré.\n LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/236/ END:VEVENT END:VCALENDAR