Abstract
Let G be a real reductive Lie group and G / H a reductive homogeneous space. We consider Kostant's cubic Dirac operator D on G / H twisted with a finite-dimensional representation of H . Under the assumption that G and H have the same complex rank, we construct a nonzero intertwining operator from principal series representations of G into the kernel of D . The Langlands parameters of these principal series are described explicitly. In particular, we obtain an explicit integral formula for certain solutions of the cubic Dirac equation D = 0 on G / H .
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