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- Applying projective functors to arbitrary holonomic simple modulesPublication . Mazorchuk, Volodymyr; Miemietz, Vanessa; Mackaay, MarcoWe prove that applying a projective functor to a holonomic simple module over a semisimple finite‐dimensional complex Lie algebra produces a module that has an essential semisimple submodule of finite length. This implies that holonomic simple supermodules over certain Lie superalgebras are quotients of modules that are induced from simple modules over the even part. We also provide some further insight into the structure of Lie algebra modules that are obtained by applying projective functors to simple modules.
- Evaluation 2-functors for Kac–Moody 2-categories of type A2Publication . Mackaay, Marco; Macpherson, James; Vaz, PedroWe construct a 2-functor from the Kac–Moody 2-category for the extended quantum affine sl3 to the homotopy 2-category of bounded chain complexes with values in the Kac–Moody 2-category for quantum gl3 , categorifying the evaluation map between the corresponding quantum Kac–Moody algebras. Our approach establishes and exploits a categorical analogue of the wellknown relation between the evaluation map and Lusztig’s internal braid group action for quantum gl3 .