The exotic nilcone of a symplectic group

Let G be the symplectic group Sp2n(k) (k an algebraically closed field of characteristic ≠2). It acts in V=k2n. The exotic nilcone of G is the nilcone, in the sense of invariant theory, of the G-module V×∧2V. The paper discusses elementary properties of the G-action on the exotic nilcone.