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Gegenbauer polynomials and the Fueter theorem

Publication at Faculty of Mathematics and Physics |
2014

Abstract

The Fueter theorem states that regular (resp. monogenic) functions in quaternionic (resp. Clifford) analysis can be constructed from holomorphic functions plane, hereby using a combination of a formal substitution and the action of an appropriate power of the Laplace operator.

In this paper we interpret this theorem on the level of representation theory, as an intertwining map between certain -modules.