Generating functions for tensor product decomposition

21st International Conference on Integrable Systems and Quantum Symmetries

Fuksa, Jan^1,2 ; Pota, Severin^1

Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Trojanova 13, 120 00 Prague, Czech Republic^1

Bogoliubov Laboratory of Theoretical Physics, JINR, Joliot-Curie 6, 141980 Dubna, Moscow region, Russia^2

关键词: Decomposition problems;    Generating functions;    Irreducible representations;    Quantum physics;    Simple operation;    State of the art;    Tensor products;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/474/1/012018/pdf
DOI  :  10.1088/1742-6596/474/1/012018

来源: IOP

【 摘 要 】

The paper deals with the tensor product decomposition problem. Tensor product decompositions are of great importance in the quantum physics. A short outline of the state of the art for the of semisimple Lie groups is mentioned. The generality of generating functions is used to solve tensor products. The corresponding generating function is rational. The feature of this technique lies in the fact that the decompositions of all tensor products of all irreducible representations are solved simultaneously. Obtaining the generating function is a difficult task in general. We propose some changes to an algorithm using Patera-Sharp character generators to find this generating function, which simplifies the whole problem to simple operations over rational functions.