Graded extensions of Verma modules

The aim of this talk is to report on some recent progress related to the classical problem of description of extensions of Verma modules in BGG category O. In particular, looking at the refined picture provided by graded extensions and using some classical results of Delorme, we determine the role the R-polynomials play in this theory. Consequently, we determine many cases in which extensions can be described by the Gabber-Joseph formula and construct explicit examples where this formula fails.

Based on a joint work with Hankyung Ko.