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<?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" "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 >"mathjaxlink" class="pcenter" ><a href="chap0.html" >[MathJax off]</a></p>"X7D2C85EC87DD46E5" name="X7D2C85EC87DD46E5" ></a></p>div class="pcenter" >h1 >hecke</h1 >div >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 >"X81488B807F2A1CF1" name="X81488B807F2A1CF1" ></a></p>on 2 or higher.</p>"X82A988D47DFAFCFA" name="X82A988D47DFAFCFA" ></a></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>"X8537FEB07AF2BEC8" name="X8537FEB07AF2BEC8" ></a></p>div class="contents" >"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 zerospan ></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 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