# Physical significance of Regge symmetry

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In the representation theory of $SU_2$ a big role is played by so-called $6-j$symbols

$$\begin{bmatrix} a & b & c\\ d & e & f\\ \end{bmatrix}.$$

There definition can be found here.

Among there  symmetries the most mysterious is a famous Regge symmetry:

$$\begin{bmatrix} a & b & c\\ d & e & f\\ \end{bmatrix}= \begin{bmatrix} a & s-b & s-c\\ d & s-e & s-f\\ \end{bmatrix},$$
where $s=\frac{b+c+e+f}{2}.$

What is the physical significance of this symmetry?  Are there any currently known applications of it?

asked Aug 31, 2018

It would be inefficient to paraphrase Philip Boalch in REGGE AND OKAMOTO SYMMETRIES which gives geometric and algebraic interpretations in chapter 2. Background. ( It is not a matrix, the Wignet encoding uses {} ). It is easy to check the symmetries with Mathematica and many other libraries or by the analyse of the Wigner formulation.

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