Pure Math Grad Student Seminar: Emily McGovern, NC State, Module categories for \text{Tilt}(SL_{2k+1}) from \tilde{A}_{n-1}-buildings
SAS 2235We 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…