Unitary lowest weight representations of the noncompact supergroup OSp(2m*/2n)

The oscillator construction of the unitary lowest weight representations of the noncompact supergroup OSp(2m*/2n) with the even subgroup SO*(2m)×USp(2n) is given. Simple rules for determining the SO*(2m)×USp(2n) decomposition of the lowest weight representations of OSp(2m*/2n) are derived. The particular examples of OSp(4*/2) with the even subgroup SU(1,1)×SU(2)×SU(2) and OSp(4*/6) with the even subgroup SU(1,1)×SU(2)×Usp(6) are studied in greater detail.