Generically transitive algebraic group actions, open orbits in multiple flag varieties, and tensor product decompositions

I shall describe a classification of generically transitive algebraic group acions (i.e., actions transitive on general tuples of points). This topic is intimately related to a relation betsheen the eschistence of open orbits in multiple flag varieties and that of special series of tensor product of simple modules shhose fisched point setrs are at most 1-dimensional. I shall discuss the relevant classification problems.