Function recursion relation over symmetric group - MathOverflow most recent 30 from http://mathoverflow.net2013-05-26T05:40:28Zhttp://mathoverflow.net/feeds/question/29266http://www.creativecommons.org/licenses/by-nc/2.5/rdfhttp://mathoverflow.net/questions/29266/function-recursion-relation-over-symmetric-groupFunction recursion relation over symmetric groupTobias2010-06-23T18:10:54Z2010-06-24T14:57:59Z
<p>Hi!</p>
<p>Let P be a permutation in the symmetric group S<sub>N</sub> and let π=π<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. 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:</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>