Clebsh-Gordan coefficients for the algebra $\mathfrak{gl}_3$ and hypergeometric functions
Representation Theory
2021-01-05 v1
Abstract
The Clebsh-Gordan coefficients for the Lie algebra in the Gelfand-Tsetlin base are calculated. In contrast to previous papers the result is given as an explicit formula. To obtain the result a realization of a representation in the space of functions on the group is used. The keystone fact that allows to carry the calculation of Clebsh-Gordan coefficients is the theorem that says that functions corresponding to Gelfand-Tsetlin base vectors can be expressed through generalized hypergeometric functions.
Keywords
Cite
@article{arxiv.2101.01049,
title = {Clebsh-Gordan coefficients for the algebra $\mathfrak{gl}_3$ and hypergeometric functions},
author = {Dmitry Artamonov},
journal= {arXiv preprint arXiv:2101.01049},
year = {2021}
}