On types for unramified p-adic unitary groups

Let F be a non-archimedean local field of residue characteristic neither 2 nor 3 equipped with a galois involution with fixed field F-0, and let G be a symplectic group over For an unramified unitary group over F-0. Following the methods of Bushnell-Kutzko for GL(N, F), we define an analogue of a simple type attached to a certain skew simple stratum, and realize a type in G. In particular, we obtain an irreducible supercuspidal representation of G like GL(N, F).