Clebsch-Gordan Coefficients for the Algebra gl3 and L-Hypergeometric Functions

Abstract

The Clebsch-Gordan coefficients for the Lie algebra gl3 in the Gelfand-Tsetlin basis are calculated. In contrast to previous works, the result is given as an explicit formula. The calculation uses a realization of a representation in the space of functions on the group GL3. The keystone fact that allows for the calculation of Clebsch-Gordan coefficients is the theorem stating that functions corresponding to Gelfand-Tsetlin base vectors can be expressed through generalized hypergeometric functions.