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

Let m n and let P(M2n,m)SLm be the algebra of all SLm(C) invariant polynomials on the spaceM2n,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. © 2007 Elsevier Inc. All rights reserved