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What is the category of representations of classical Lie algebras of "infinite rank"?

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Ivan Penkov
Jacobs University, Bremen
Die, 2018-05-08 14:00 - 15:00
MPIM Lecture Hall

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.

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