Abstract
In the construction of the general SU(5) states, the action of each individual lowering operators (raised to a power) operating on the semimaximal state leads to an operator-valued polynomial which is shown to belong to the class of generalized hypergeometric functions in the sense of Gel'fand (namely, they are Radon transform of linear forms). Three new functions are found at the SU(5) level and their content in terms of known lower-hierarchy functions are explicitly exhibited. The structure of the general SU(n) states due to the combined action of all lowering operators is quite complicated, but the action of each individual lowering operator taken one at a time may still be manageable for higher n, and, in the spirit of boson operator formalism, this may be one systematical way of producing high-hierarchy generalized hypergeometric functions.
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