The second order pole over split quaternions

30th International Colloquium on Group Theoretical Methods in Physics

Libine, Matvei^1

Department of Mathematics, Indiana University, Rawles Hall, 831 East 3rd St, Bloomington

IN

47405, United States^1

关键词: Irre-ducible components;    Lie Algebra;    Quaternionic analysis;    Representation theory;    Second orders;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/597/1/012056/pdf
DOI  :  10.1088/1742-6596/597/1/012056

来源: IOP

【 摘 要 】

This is an addition to a series of papers [1, 2, 3, 4], where we develop quaternionic analysis from the point of view of representation theory of the conformal Lie group and its Lie algebra. In this paper we develop split quaternionic analogues of certain results from [4]. Thus we introduce a space of functions Dh⊕ Dawith a natural action of the Lie algebra gl(2, HC)sl(4, C), decompose Dh⊕ Dainto irreducible components and find the gl(2, Hc)- equivariant projectors onto each of these irreducible components.