Symmetries of slice monogenic functions

  • Fabrizio Colombo

    Politecnico di Milano, Italy
  • Rolf Sören Kraußhar

    Universität Erfurt, Germany
  • Irene Sabadini

    Politecnico di Milano, Italy
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In this paper we consider the symmetry behavior of slice monogenic functions under Möbius transformations. We describe the group under which slice monogenic functions are taken into slice monogenic functions. We prove a transformation formula for composing slice monogenic functions with Möbius transformations and describe their conformal invariance. Finally, we explain two construction methods to obtain automorphic forms in the framework of this function class. We round off by presenting a precise algebraic characterization of the subset of slice monogenic linear fractional transformations within the set of general Möbius transformations.

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Fabrizio Colombo, Rolf Sören Kraußhar, Irene Sabadini, Symmetries of slice monogenic functions. J. Noncommut. Geom. 14 (2020), no. 3, pp. 1075–1106

DOI 10.4171/JNCG/387