Principal series representations and harmonic spinors
| Autor: | S. Mehdi, Roger Zierau |
|---|---|
| Rok vydání: | 2006 |
| Předmět: |
Mathematics(all)
Pure mathematics Spinor Series (mathematics) General Mathematics Lie group Dirac algebra Clifford analysis Principal series representations Dirac operator Cubic Dirac operator Algebra symbols.namesake Dirac equation Homogeneous space Reductive homogeneous spaces symbols Harmonic spinors Mathematics |
| Zdroj: | Advances in Mathematics. 199:1-28 |
| ISSN: | 0001-8708 |
| DOI: | 10.1016/j.aim.2004.10.021 |
| Popis: | 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 . |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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