(g,K)-modules over commutative rings and related geometry

I am working on representation theory of Lie groups. My main research interest is on (g,K)-modules over commutative rings and related geometry. Recently, I have worked on geometry of partial flag schemes of reductive group schemes and twisted D-modules on them. In particular, I construct and study arithmetic models of cohomologically induced modules. I also work on contraction families which are certain (group) schemes over the polynomial ring and on representation theory of algebraic supergroups over non separably closed fields of characteristic not two (e.g. the field of real numbers). They are closely related to mathematical physics.