Function recursion relation over symmetric group - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-26T05:40:28Z http://mathoverflow.net/feeds/question/29266 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/29266/function-recursion-relation-over-symmetric-group Function recursion relation over symmetric group Tobias 2010-06-23T18:10:54Z 2010-06-24T14:57:59Z <p>Hi!</p> <p>Let P be a permutation in the symmetric group S<sub>N</sub> and let &pi;=&pi;<sub>j, j+1</sub> be a transposition of elements j and j+1 of the permutation. Let A(P) be a function in dependence of the permutation P. P&pi; 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:</p> <p>$$\frac{A(P\pi)}{A(P)} = - \exp(-i(k_{p_j}- k_{p_{j+1}}))$$</p> <p>k<sub>j</sub> are numbers, and $p_j$ is the j-th element of the permutation.</p> <p>I hope someone can give me a hint or advice to solve this.</p> <p>Tobias</p>