Covariants of Spn(C) and degenerate principal series of GLn(H)

Let m⩽n and let PSLm(M2n,m) be the algebra of all SLm(C) invariant polynomials on the space M2n,m of all 2n×m complex matrices. We determine the free generators of its subalgebra of Spn(C) covariants. These generators are given as pfaffians. They are used to study the degenerate principal series representations of GLn(H) induced from characters of a maximal parabolic subgroup. We determine the composition series and unitarity of these representations.