<?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>schurModulesMap -- creates a map between two Schur modules via the specified function.</title>
<link rel="stylesheet" type="text/css" href="../../../../Macaulay2/Style/doc.css"/>
</head>
<body>
<table class="buttons">
<tr>
<td><div><a href="_split__Character.html">next</a> | <a href="_schur__Module.html">previous</a> | <a href="_split__Character.html">forward</a> | <a href="_schur__Module.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>schurModulesMap -- creates a map between two Schur modules via the specified function.</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>schurModulesMap(N,M,F)</tt></div>
</dd></dl>
</div>
</li>
<li><div class="single">Inputs:<ul><li><span><tt>N</tt>, <span>a <a href="../../Macaulay2Doc/html/___Module.html">module</a></span>, Schur module</span></li>
<li><span><tt>M</tt>, <span>a <a href="../../Macaulay2Doc/html/___Module.html">module</a></span>, Schur module</span></li>
<li><span><tt>F</tt>, <span>a <a href="../../Macaulay2Doc/html/___Function.html">function</a></span>, The function should specify, for every SST in the basis of M, a linear comination of tableaus of the shape specified by N. The output of F should be a sequence of pairs (c,T) where c is a coefficient in ring(N) and T a tableau (not necessarily semistandard).</span></li>
</ul>
</div>
</li>
<li><div class="single">Outputs:<ul><li><span><tt>G</tt>, <span>a <a href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span>, A map between M and N.</span></li>
</ul>
</div>
</li>
</ul>
</div>
<div class="single"><h2>Description</h2>
<div><div>Constructs the map between M and N specified by the function F.</div>
<table class="examples"><tr><td><pre>i1 : n = 4; --j-th differential of the Koszul Complex on the variables of R</pre>
</td></tr>
<tr><td><pre>i2 : j = 2;</pre>
</td></tr>
<tr><td><pre>i3 : mu1=apply(j,j->1)
o3 = {1, 1}
o3 : List</pre>
</td></tr>
<tr><td><pre>i4 : mu2=apply(j+1,j->1)
o4 = {1, 1, 1}
o4 : List</pre>
</td></tr>
<tr><td><pre>i5 : R = QQ[x_1..x_n];</pre>
</td></tr>
<tr><td><pre>i6 : M=schurModule(mu1,R^n);</pre>
</td></tr>
<tr><td><pre>i7 : N=schurModule(mu2,R^n);</pre>
</td></tr>
<tr><td><pre>i8 : F = T -> apply(numgens R, j -> (R_j, augmentFilling(T,0,j)))
o8 = F
o8 : FunctionClosure</pre>
</td></tr>
<tr><td><pre>i9 : schurModulesMap(N,M,F)
o9 = | x_3 -x_2 x_1 0 0 0 |
| x_4 0 0 -x_2 x_1 0 |
| 0 x_4 0 -x_3 0 x_1 |
| 0 0 x_4 0 -x_3 x_2 |
4 6
o9 : Matrix R <--- R</pre>
</td></tr>
</table>
</div>
</div>
<div class="single"><h2>Caveat</h2>
<div><div>The function F should output lists of pairs where the second component is a filling of the partition corresponding to N.</div>
</div>
</div>
<div class="single"><h2>See also</h2>
<ul><li><span><a href="_schur.html" title="creates a map between Schur modules">schur</a> -- creates a map between Schur modules</span></li>
</ul>
</div>
<div class="waystouse"><h2>Ways to use <tt>schurModulesMap</tt> :</h2>
<ul><li>schurModulesMap(Module,Module,Function)</li>
</ul>
</div>
</div>
</body>
</html>
