Principal series representations and harmonic spinors |
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Authors: | S Mehdi |
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Institution: | a School of Mathematics, Tata Institute of Fundamental Research, Mumbai 400005, India b Mathematics Department, Oklahoma State University, Stillwater, Oklahoma 74078, USA |
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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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Keywords: | Cubic Dirac operator Harmonic spinors Reductive homogeneous spaces Principal series representations |
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