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Pure Math Grad Student Seminar: Emily McGovern, NC State, Module categories for \text{Tilt}(SL_{2k+1}) from \tilde{A}_{n-1}-buildings
September 19, 2022 | 3:00 pm - 4:00 pm EDT
We show that the category of vector bundles over the vertices of a locally finite \tilde{A}_{n-1} building \Delta, Vec(\Delta), has the structure of a Tilt(SL_{2k+1}) module category. This module category is the q-analogue of the Tilt(SL_{2k+1}) action on vector bundles over the sl_n weight lattice. Our construction of the Tilt(SL_{2k+1}) action on Vec(\Delta) extends to Vec(\Delta)^{G}, its equivariantization, which gives us a class of non-standard Tilt(SL_{2k+1}) module categories. When G acts simply transitively, recovers the fiber functors of \cite{Jones21}.
Zoom Meeting link: https://ncsu.zoom.us/j/95923219557?pwd=T3MzUEZRazRaY2tBdjl1dFVJOG50QT09