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<head><title>character -- Determines the character of a compostion of schur functors applied to the representation of GL(V) on V</title>
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<div><h1>character -- Determines the character of a compostion of schur functors applied to the representation of GL(V) on V</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>character(L,d)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>L</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, A nested list whose entries are partitions</span></li>
<li><span><tt>d</tt>, <span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, An integer</span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>p</tt>, <span>a <a href="../../Macaulay2Doc/html/___Ring__Element.html">ring element</a></span>, A symmetric polynomial</span></li>
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<div class="single"><h2>Description</h2>
<div><div>Given a list L of partitions L1,...,Ln computes the character of the composition of Schur functors SL1(SL2(...(SLn(V)))) applied to the canonical representation of GL(V) where dim(V)=d</div>
<table class="examples"><tr><td><pre>i1 : character({{1,1,1},{2}},4)--The GL(4) action on the grassmannian of 3-dimensional subspaces of quadrics in four variables
3 3 4 3 2 2 3 4 3 2 2 2 2 3 2
o1 = x x + x x x + 2x x x + 2x x x + x x x + 2x x x + 2x x x + 2x x x
0 1 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2
------------------------------------------------------------------------
3 3 2 3 2 3 3 3 4 4 3 2 2 3
+ x x + 2x x x + 2x x x + x x + x x x + x x x + 2x x x + 2x x x
0 2 0 1 2 0 1 2 1 2 0 1 2 0 1 3 0 1 3 0 1 3
------------------------------------------------------------------------
4 4 3 2 2 3 4 3 2
+ x x x + x x x + 4x x x x + 5x x x x + 4x x x x + x x x + 2x x x
0 1 3 0 2 3 0 1 2 3 0 1 2 3 0 1 2 3 1 2 3 0 2 3
------------------------------------------------------------------------
2 2 2 2 3 2 2 3 3 2 3
+ 5x x x x + 5x x x x + 2x x x + 2x x x + 4x x x x + 2x x x +
0 1 2 3 0 1 2 3 1 2 3 0 2 3 0 1 2 3 1 2 3
------------------------------------------------------------------------
4 4 3 2 2 2 2 3 2 3 2 2 2
x x x + x x x + 2x x x + 2x x x + 2x x x + 2x x x + 5x x x x +
0 2 3 1 2 3 0 1 3 0 1 3 0 1 3 0 2 3 0 1 2 3
------------------------------------------------------------------------
2 2 3 2 2 2 2 2 2 2 2 2 3 2 3 2
5x x x x + 2x x x + 2x x x + 5x x x x + 2x x x + 2x x x + 2x x x
0 1 2 3 1 2 3 0 2 3 0 1 2 3 1 2 3 0 2 3 1 2 3
------------------------------------------------------------------------
3 3 2 3 2 3 3 3 2 3 3 2 3
+ x x + 2x x x + 2x x x + x x + 2x x x + 4x x x x + 2x x x +
0 3 0 1 3 0 1 3 1 3 0 2 3 0 1 2 3 1 2 3
------------------------------------------------------------------------
2 3 2 3 3 3 4 4 4
2x x x + 2x x x + x x + x x x + x x x + x x x
0 2 3 1 2 3 2 3 0 1 3 0 2 3 1 2 3
o1 : R</pre>
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<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>
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<div class="waystouse"><h2>Ways to use <tt>character</tt> :</h2>
<ul><li>character(List,ZZ)</li>
</ul>
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