Abstract
The paper aims at proving general duality theorems for Hermitian Hurwitz pairs (abbreviated as HHP), related to the generalized Dirac or Fueter equations, and gives comparison theorems for solutions of #-self adjoint Dirac or Fueter equations, where #-self adjointness implies the self adjointness with respect to certain indefinite metrics. In low-dimensional cases these duality theorems can be described in a more explicit manner. Namely, we can get dualities between the Minkowski space-time with signature(+, − − −) and the neutral space with signature (++, −−) related to the Penrose theory. We can also get the dualities between the Neveu-Schwarz model with (+,−) and the holomorphic-antiholomorphic model with (−, −). These dualities can be described in terms of the Wick rotations. We notice that the Wick rotation cannot be used directly because our Dirac operators are #-self adjoint, while the Wick rotations break down this property.
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Research of the first author partially supported by the State Committee for Scientific Research (KBN) grant PB 2 P03A 016 10.
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Lawrynowicz, J., Suzuki, O. Hurwitz duality theorems for Fueter and Firac equations. AACA 7, 113–132 (1997). https://doi.org/10.1007/BF03041222
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DOI: https://doi.org/10.1007/BF03041222