Hi!

Let P be a permutation in the symmetric group S_{N} and let π=π_{j, j+1} be a transposition of elements j and j+1 of the permutation. Let A(P) be a function in dependence of the permutation P. Pπ is the permutation P with elements j and j+1 switched. I need to get an explicit expression of A(P) for the recursion relation:

$$\frac{A(P\pi)}{A(P)} = - \exp(-i(k_{p_j}- k_{p_{j+1}}))$$

k_{j} are numbers, and $p_j$ is the j-th element of the permutation.

I hope someone can give me a hint or advice to solve this.

Tobias