products/sources/formale Sprachen/GAP/pkg/lins/gap/   (Algebra von RWTH Aachen Version 4.15.1©)  Datei vom 15.2.2024 mit Größe 7 kB image not shown  

Quelle  chap0_mj.html   Sprache: unbekannt

 
<?xml version="1.0" encoding="UTF-8"?>

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
         "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">

<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en">
<head>
<script type="text/javascript"
  src="https://cdn.jsdelivr.net/npm/mathjax@2/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
</script>
<title>GAP (hecke) - Contents</title>
<meta http-equiv="content-type" content="text/html; charset=UTF-8" />
<meta name="generator" content="GAPDoc2HTML" />
<link rel="stylesheet" type="text/css" href="manual.css" />
<script src="manual.js" type="text/javascript"></script>
<script type="text/javascript">overwriteStyle();</script>
</head>
<body class="chap0"  onload="jscontent()">


<div class="chlinktop"><span class="chlink1">Goto Chapter: </span><a href="chap0_mj.html">Top</a>  <a href="chap1_mj.html">1</a>  <a href="chap2_mj.html">2</a>  <a href="chap3_mj.html">3</a>  <a href="chapBib_mj.html">Bib</a>  <a href="chapInd_mj.html">Ind</a>  </div>

<div class="chlinkprevnexttop"> <a href="chap0_mj.html">[Top of Book]</a>   <a href="chap0_mj.html#contents">[Contents]</a>    <a href="chap1_mj.html">[Next Chapter]</a>   </div>

<p id="mathjaxlink" class="pcenter"><a href="chap0.html">[MathJax off]</a></p>
<p><a id="X7D2C85EC87DD46E5" name="X7D2C85EC87DD46E5"></a></p>
<div class="pcenter">

<h1>hecke</h1>


<h2>Calculating decomposition matrices of Hecke algebras</h2>

<p>
    1.5.4</p>

<p>
    27 August 2024
  </p>

</div>
<p><b>
    Dmitriy Traytel



  </b>
<br />Email: <span class="URL"><a href="mailto:traytel@in.tum.de">traytel@in.tum.de</a></span>
<br />Homepage: <span class="URL"><a href="https://home.in.tum.de/~traytel/hecke/">https://home.in.tum.de/~traytel/hecke/</a></span>
</p>

<p><a id="X81488B807F2A1CF1" name="X81488B807F2A1CF1"></a></p>
<h3>Copyright</h3>
<p>© 2010–2013 by Dmitriy Traytel</p>

<p>This package may be distributed under the terms and conditions of the GNU Public License Version 2 or higher.</p>

<p><a id="X82A988D47DFAFCFA" name="X82A988D47DFAFCFA"></a></p>
<h3>Acknowledgements</h3>
<p><strong class="pkg">Hecke</strong> is a port of the <strong class="pkg">GAP</strong> 3 package <strong class="pkg">Specht</strong> 2.4 to <strong class="pkg">GAP</strong> 4. <strong class="pkg">Specht</strong> 2.4 was written by Andrew Mathas, who allowed Dmitriy Traytel to use his source code as the basis for <strong class="pkg">hecke</strong>.</p>

<p><a id="X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8"></a></p>

<div class="contents">
<h3>Contents<a id="contents" name="contents"></a></h3>

<div class="ContChap"><a href="chap1_mj.html#X7CD78FC183A57690">1 <span class="Heading">Decomposition numbers of Hecke algebras of type A</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X7BBCB13F82ACC213">1.1 <span class="Heading">Description</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X7A3BD2F77A4AC7EA">1.2 <span class="Heading">The modular representation theory of Hecke algebras</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X8226F6F77ACF26D8">1.3 <span class="Heading">Two small examples</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X786BACDB82918A65">1.4 <span class="Heading">Overview over this manual</span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X8779AFAF8411A26A">1.5 <span class="Heading">Credits</span></a>
</span>
</div>
</div>
<div class="ContChap"><a href="chap2_mj.html#X79845447824F3333">2 <span class="Heading">Installation of the <strong class="pkg">hecke</strong>-Package</span></a>
</div>
<div class="ContChap"><a href="chap3_mj.html#X7ED1AB5C7E41D277">3 <span class="Heading">Specht functionality</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X78AA2DBD7D5D3F02">3.1 <span class="Heading">Porting notes</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X8340A4F97986693C">3.1-1 <span class="Heading">Structure of <strong class="pkg">Hecke</strong></span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X8120A27282B82CC8">3.1-2 <span class="Heading">Renamings</span></a>
</span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X7A7DF4FC796EF66F">3.2 <span class="Heading">Specht functions</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7FE26921867C440A">3.2-1 Specht</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X8037763587274161">3.2-2 <span class="Heading">Simple information access</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7C92700882971537">3.2-3 <span class="Heading">The functions MakeSpecht, MakePIM and MakeSimple</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X86F599A07A7C1C33">3.2-4 <span class="Heading">Decomposition numbers of the symmetric groups</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X838BEC0382BF87EA">3.2-5 <span class="Heading">Hecke algebras over fields of positive characteristic</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X83009CE685621BD4">3.2-6 <span class="Heading">The Fock space and Hecke algebras over fields of characteristic zero
</span></a>
</span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7B57DF517F73F00D">3.2-7 Schur</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X84F0F9E47D5EEBCF">3.2-8 DecompositionMatrix</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7F616CCE808FA11E">3.2-9 CrystalDecompositionMatrix</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X829A23A97EE4C20E">3.2-10 DecompositionNumber</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X7C5B169286EFC900">3.3 <span class="Heading">Partitions in <strong class="pkg">Hecke</strong></span></a>
</span>
</div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X87A6E8DD85F3F020">3.4 <span class="Heading">Inducing and restricting modules</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X81D7F7A4812BB04D">3.4-1 RInducedModule</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X780709B3865BC344">3.4-2 SInducedModule</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X783BC74E81A7D0E6">3.4-3 RRestrictedModule</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X8041ABFA86D7A3EF">3.4-4 SRestrictedModule</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X79F430837BA7BAD2">3.5 <span class="Heading">Operations on decomposition matrices</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7D257389845738DB">3.5-1 InducedDecompositionMatrix</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X803A99987E501AC9">3.5-2 IsNewIndecomposable</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X802E811683E611EE">3.5-3 InvertDecompositionMatrix</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X87B18FD97B2D8E80">3.5-4 AdjustmentMatrix</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X78B0FF2079269138">3.5-5 SaveDecompositionMatrix</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X84DD2D517FC1F905">3.5-6 CalculateDecompositionMatrix</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7FDC65328102C1B9">3.5-7 MatrixDecompositionMatrix</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X86EBEBF680EBC98E">3.5-8 DecompositionMatrixMatrix</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7B05627D83E6977E">3.5-9 AddIndecomposable</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X79FA055E8250E6A2">3.5-10 RemoveIndecomposable</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X8434DC7C8364CB54">3.5-11 MissingIndecomposables</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X7A697AAA799BA7D4">3.6 <span class="Heading">Calculating dimensions</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X828528747E4AC4C9">3.6-1 SimpleDimension</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7B98631580E193BB">3.6-2 SpechtDimension</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X78F1DC277875BAFD">3.7 <span class="Heading">Combinatorics on Young diagrams</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X820A908F8337F59C">3.7-1 Schaper</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7FB82B3184287362">3.7-2 IsSimpleModule</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7A6262B684185E3D">3.7-3 MullineuxMap</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7CC6C04482DD1E9D">3.7-4 MullineuxSymbol</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7826922879DD8D8A">3.7-5 PartitionMullineuxSymbol</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7CE4D6487FD009B1">3.7-6 GoodNodes</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X783B52458335975F">3.7-7 NormalNodes</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X85B290977A17D9EE">3.7-8 GoodNodeSequence</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7B704FE781A311E5">3.7-9 PartitionGoodNodeSequence</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7A9DC101850008A2">3.7-10 GoodNodeLatticePath</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7918D9DE7ACE2294">3.7-11 LittlewoodRichardsonRule</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7B9901427D1CF6F4">3.7-12 InverseLittlewoodRichardsonRule</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X790D4ACF7930340F">3.7-13 EResidueDiagram</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7DE3773C78BC324C">3.7-14 HookLengthDiagram</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7F2ACCBF788A62E8">3.7-15 RemoveRimHook</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7CEA98C779BDBD1A">3.7-16 AddRimHook</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X8350934A7F9AB5BE">3.8 <span class="Heading">Operations on partitions</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X867496487DC35776">3.8-1 ECore</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X8236220C87814790">3.8-2 IsECore</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X8538AAAF8628A725">3.8-3 EQuotient</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7F357B417D495B6F">3.8-4 CombineEQuotientECore</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7C460635829E7ED0">3.8-5 EWeight</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X86308F6C818B220C">3.8-6 ERegularPartitions</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7BEDA8F286ED5F20">3.8-7 IsERegular</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7D131AF0839089BD">3.8-8 ConjugatePartition</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X8711CC56792711A7">3.8-9 PartitionBetaSet</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7EC4D0FA81B55391">3.8-10 ETopLadder</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X820388EF7C8333BA">3.8-11 Dominates</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X84DB1DD37AF227CF">3.8-12 LengthLexicographic</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X8480188D81ECBD92">3.8-13 Lexicographic</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X78F41DF77D6F8292">3.8-14 ReverseDominance</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X83890936806E3A34">3.9 <span class="Heading">Miscellaneous functions on modules</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7A8E810C85A62DD6">3.9-1 Specialized</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X8232C0A1846A27FB">3.9-2 ERegulars</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X822E8193835DD1D9">3.9-3 SplitECores</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7E92948B80075E46">3.9-4 Coefficient</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X79FB3FE67D55BCFA">3.9-5 InnerProduct</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap3_mj.html#X7D473E167C866CEC">3.10 <span class="Heading">Semi-standard and standard tableaux</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7F0F9663796E6978">3.10-1 Tableau</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X79ADB1B980D12A14">3.10-2 SemiStandardTableaux</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7E51D6107DBE2A74">3.10-3 StandardTableaux</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7869DA9A8198BD28">3.10-4 ConjugateTableau</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7E5351C27C9253D9">3.10-5 ShapeTableau</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap3_mj.html#X7CABF92D7BF07DD1">3.10-6 TypeTableau</a></span>
</div></div>
</div>
<div class="ContChap"><a href="chapBib_mj.html"><span class="Heading">References</span></a></div>
<div class="ContChap"><a href="chapInd_mj.html"><span class="Heading">Index</span></a></div>
<br />
</div>

<div class="chlinkprevnextbot"> <a href="chap0_mj.html">[Top of Book]</a>   <a href="chap0_mj.html#contents">[Contents]</a>    <a href="chap1_mj.html">[Next Chapter]</a>   </div>


<div class="chlinkbot"><span class="chlink1">Goto Chapter: </span><a href="chap0_mj.html">Top</a>  <a href="chap1_mj.html">1</a>  <a href="chap2_mj.html">2</a>  <a href="chap3_mj.html">3</a>  <a href="chapBib_mj.html">Bib</a>  <a href="chapInd_mj.html">Ind</a>  </div>

<hr />
<p class="foot">generated by <a href="https://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc">GAPDoc2HTML</a></p>
</body>
</html>

100%


[ zur Elbe Produktseite wechseln0.18Quellennavigators  Analyse erneut starten  ]

                                                                                                                                                                                                                                                                                                                                                                                                     

Neuigkeiten

     Aktuelles
     Motto des Tages

Software

     Produkte
     Quellcodebibliothek

Aktivitäten

     Artikel über Sicherheit
     Anleitung zur Aktivierung von SSL

Muße

     Gedichte
     Musik
     Bilder
Jenseits des Üblichen ....

Besucherstatistik

Besucherstatistik

Monitoring

Montastic status badge