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<head><title>BGG -- Bernstein-Gel'fand-Gel'fand correspondence</title>
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<div><h1>BGG -- Bernstein-Gel'fand-Gel'fand correspondence</h1>
<div class="single"><h2>Description</h2>
<div>The Bernstein-Gel'fand-Gel'fand correspondence is an isomorphism between the derived category of bounded complexes of finitely generated modules over a polynomial ring and the derived category of bounded complexes of finitely generated module over an exterior algebra (or of certain Tate resolutions). This package implements routines for investigating the BGG correspondence.<p/>
More details can be found in <a href="http://www.math.uiuc.edu/Macaulay2/Book/">Sheaf Algorithms Using Exterior Algebra</a>.</div>
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<div class="single"><h2>Authors</h2>
<ul><li><div class="single"><a href="http://www.webpages.uidaho.edu/~abo/">Hirotachi Abo</a><span> <<a href="mailto:abo@uidaho.edu">abo@uidaho.edu</a>></span></div>
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<li><div class="single"><a href="http://www.math.uni-sb.de/ag/decker/">Wolfram Decker</a><span> <<a href="mailto:decker@math.uni-sb.de">decker@math.uni-sb.de</a>></span></div>
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<li><div class="single"><a href="http://www.msri.org/~de/">David Eisenbud</a><span> <<a href="mailto:de@msri.org">de@msri.org</a>></span></div>
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<li><div class="single"><a href="http://www.math.uni-sb.de/ag/schreyer/">Frank Schreyer</a><span> <<a href="mailto:schreyer@math.uni-sb.de">schreyer@math.uni-sb.de</a>></span></div>
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<li><div class="single"><a href="http://www.mast.queensu.ca/~ggsmith/">Gregory G. Smith</a><span> <<a href="mailto:ggsmith@mast.queensu.ca">ggsmith@mast.queensu.ca</a>></span></div>
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<li><div class="single"><a href="http://www.math.cornell.edu/~mike/">Mike Stillman</a><span> <<a href="mailto:mike@math.cornell.edu">mike@math.cornell.edu</a>></span></div>
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<div class="single"><h2>Version</h2>
This documentation describes version <b>1.0</b> of BGG.</div>
<div class="single"><h2>Source code</h2>
The source code from which this documentation is derived is in the file <a href="../../../../Macaulay2/BGG.m2">BGG.m2</a>.</div>
<div class="single"><h2>Exports</h2>
<ul><li><div class="single">Functions<ul><li><span><a href="_beilinson.html" title="Vector bundle map associated to the Beilinson monad">beilinson</a> -- Vector bundle map associated to the Beilinson monad</span></li>
<li><span><a href="_bgg.html" title="the ith differential of the complex R(M)">bgg</a> -- the ith differential of the complex R(M)</span></li>
<li><span><a href="_cohomology__Table.html" title="dimensions of cohomology groups">cohomologyTable</a> -- dimensions of cohomology groups</span></li>
<li><span><a href="_sym__Ext.html" title="the first differential of the complex R(M)">symExt</a> -- the first differential of the complex R(M)</span></li>
<li><span><a href="_tate__Resolution.html" title="finite piece of the Tate resolution">tateResolution</a> -- finite piece of the Tate resolution</span></li>
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