<?xml version="1.0" encoding="utf-8" ?> <!-- for emacs: -*- coding: utf-8 -*- --> <!-- Apache may like this line in the file .htaccess: AddCharset utf-8 .html --> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0 plus SVG 1.1//EN" "http://www.w3.org/2002/04/xhtml-math-svg/xhtml-math-svg-flat.dtd" > <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en"> <head><title>schurRank -- computes the dimension of the irreducible GL(QQ^n) representation associated to a partition</title> <link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/> </head> <body> <table class="buttons"> <tr> <td><div><a href="_standard__Tableaux.html">next</a> | <a href="_pure__Free.html">previous</a> | <a href="_standard__Tableaux.html">forward</a> | <a href="_pure__Free.html">backward</a> | up | <a href="index.html">top</a> | <a href="master.html">index</a> | <a href="toc.html">toc</a> | <a href="http://www.math.uiuc.edu/Macaulay2/">Macaulay2 web site</a></div> </td> </tr> </table> <hr/> <div><h1>schurRank -- computes the dimension of the irreducible GL(QQ^n) representation associated to a partition</h1> <div class="single"><h2>Synopsis</h2> <ul><li><div class="list"><dl class="element"><dt class="heading">Usage: </dt><dd class="value"><div><tt>schurRank(n, mu)</tt></div> </dd></dl> </div> </li> <li><div class="single">Inputs:<ul><li><span><tt>n</tt>, <span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, the size of the matrix group GL(QQ^n)</span></li> <li><span><tt>mu</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, a partition (mu_1, ..., m_r) where mu_i is the number of boxes in the ith row</span></li> </ul> </div> </li> <li><div class="single">Outputs:<ul><li><span><span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, The dimension of the irreducible GL(QQ^n) representation associated to mu</span></li> </ul> </div> </li> </ul> </div> <div class="single"><h2>Description</h2> <div>The dimension is computed using the determinantal formula given by the Weyl character formula.<table class="examples"><tr><td><pre>i1 : schurRank(5, {4,3}) -- should be 560 o1 = 560</pre> </td></tr> </table> </div> </div> <div class="single"><h2>See also</h2> <ul><li><span><a href="_standard__Tableaux.html" title="list all standard tableaux of a certain shape with bounded labels">standardTableaux</a> -- list all standard tableaux of a certain shape with bounded labels</span></li> </ul> </div> <div class="waystouse"><h2>Ways to use <tt>schurRank</tt> :</h2> <ul><li>schurRank(ZZ,List)</li> </ul> </div> </div> </body> </html>