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Article

Cheng, Wanqing ; Ding, Chao
On a higher spin generalization of the complex $\Pi $-operator. (English). Archivum Mathematicum, vol. 62 (2026), issue 3, pp. 89-111
MSC: 30G20, 30G35, 35A22 | DOI: 10.5817/AM2026-3-89
Keywords:
Rarita-Schwinger operator; integral transform; higher spin $\Pi $-operator; higher spin Beltrami equation
Summary:
Rarita-Schwinger fields are solutions to the relativistic field equation of spin-$3/2$ fermions in four dimensional flat spacetime, which are important in supergravity and superstring theories. Bureš et al. generalized it to arbitrary spin $k/2$ in 2002 in the context of Clifford algebras. In this article, we introduce a higher spin $\Pi $-operator related to the Rarita-Schwinger operator. Further, we investigate norm estimates, mapping properties and the adjoint operator of the higher spin $\Pi $-operator. As an application, a higher spin Beltrami equation is introduced, and existence and uniqueness of solutions to this higher spin Beltrami equation is established by the norm estimate of the higher spin $\Pi $-operator.
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