zbMATH — the first resource for mathematics

Higher monogenicity and residue theorem for Rarita-Schwinger operator. (English) Zbl 1055.53036
Slovák, Jan (ed.) et al., The proceedings of the 23th winter school “Geometry and physics”, Srní, Czech Republic, January 18–25, 2003. Palermo: Circolo Matemàtico di Palermo. Suppl. Rend. Circ. Mat. Palermo, II. Ser. 72, 177-191 (2004).
The author investigates various properties of higher spin analogy of Clifford analysis [cf. R. Delanghe, F. Sommen and V. Soucek, Clifford algebra and spinor-valued functions. A function theory for the Dirac operator. (Mathematics and its Applications 53, Kluwer Academic Publishers, Dordrecht) (1992; Zbl 0747.53001)].
In particular, he employs representation theory (Littlewood-Richardson rule) to get decompositions on irreducibles of various tensor-spinor Spin-modules. Based on these results he defines the Rarita-Schwinger operator, which is a higher spin analog of the Dirac operator in Clifford analysis. He then proceeds to define higher spin (i.e. Rarita-Schwinger) monogenic functions. This notion is used in the definition of the algebraic operators on \(S_{3/2}\)-valued differential forms and the statements of Stokes and residue theorems for \(S_{3/2}\)-valued monogenic functions.
For the entire collection see [Zbl 1034.53002].
Reviewer: Ioan Pop (Iaşi)
53C27 Spin and Spin\({}^c\) geometry
53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions