Clebsh–Gordan coefficients for the algebra 𝔤𝔩₃ and hypergeometric functions

Artamonov, D.

doi:10.1090/spmj/1686

Clebsh–Gordan coefficients for the algebra $\mathfrak {gl}_3$ and hypergeometric functions
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by D. V. Artamonov
Translated by: the author

St. Petersburg Math. J. 33 (2022), 1-22

DOI: https://doi.org/10.1090/spmj/1686

Published electronically: December 28, 2021

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Abstract:

The Clebsh–Gordan coefficients for the Lie algebra $\mathfrak {gl}_3$ 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 $GL_3$ is used. The keystone fact that allows one to carry the calculation of Clebsh–Gordan coefficients is the theorem that says that functions corresponding to the Gelfand–Tsetlin base vectors can be expressed in terms of generalized hypergeometric functions.

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