On the Combinatorial Structure of State Vectors in U(n). II. The Generalization of Hypergeometric Functions on U(n) States
- 1 September 1969
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 10 (9), 1635-1646
- https://doi.org/10.1063/1.1665011
Abstract
The derivation of the explicit algebraic expressions of the SU(n) state vectors in the boson‐operator realization is shown to lead to a generalization of hypergeometric functions. The SU(3) state vectors are rederived by the combinatorial method‐propounded in Paper I [J. Math. Phys. 10, 221 (1969)] of this series of papers‐and are shown to be represented by a hypergeometric distribution function and an associated generalization of the Young tableaux calculus. The SU(4) state vectors are also derived to demonstrate the main features of the general U(n) state vectors. The SU(4) state vectors are expressed in terms of the constituents of Radon transforms.Keywords
This publication has 3 references indexed in Scilit:
- Combinatorial Structure of State Vectors in Un. I. Hook Patterns for Maximal and Semimaximal States in UnJournal of Mathematical Physics, 1969
- Operators that Lower or Raise the Irreducible Vector Spaces of U n−1 Contained in an Irreducible Vector Space of UnJournal of Mathematical Physics, 1965
- On the Representations of the Semisimple Lie Groups. IIJournal of Mathematical Physics, 1963