The classical Lie algebras sl, so, sp "of infinite rank" in the naive sense have uncountably many nonconjugate Borel subalgebras. Therefore the definition of categories of their representations involves choices. A natural choice is a Dynkin Borel subalgebra. In this talk, I will advocate for another choice, namely that of a perfect Borel subalgebra. In addition, I will impose the condition of large local annihilator on the objects of the category. The resulting category is a nice highest-weight category with standard objects, but without costandard objects. I will discuss the basic features of this category. This is a Joint work with Vera Serganova.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/5312