SL(2) intertwining Minkowski valuations in the plane

Abstract The polygon valued Minkowski valuations in R 2 intertwining with the special linear group are completely classified in this paper without any additional assumptions. Our results characterize projection bodies and difference bodies in R 2 . There are also some SL ( 2 ) intertwining Minkowski valuations that can only be defined in R 2 . It somehow suggests why such classification problems are more complicated than higher dimensional spaces.