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AMS-MML_HTMLorMML">8 " />/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>ml#contents">[Contents]</a> <a href="chap1_mj.html">[Next Chapter]</a> </div>1 .8 .4 </p>11 January 2024 nitn.it</a></span>http://www.science.unitn.it/~degraaf ">http://www.science.unitn.it/~degraaf</a></span>2002 Willem A. de Graaf</p>1 <span class="Heading">Introduction</span></a>2 <span class="Heading">Background</span></a>#X7AAC838B7CEB5E54">2 .1 <span class="Heading">Gaussian Binomials</span></a>#X81394E207F6AA6CF">2 .2 <span class="Heading">Quantized enveloping algebras</span></a>#X7DCC28DE7C626D33">2 .3 <span class="Heading">Representations of <span class="SimpleMath">\(U_q(\mathfrak{g})\)</span> </span></a>#X83E7F39F7D16793B">2 .4 <span class="Heading">PBW-type bases </span></a>#X798D979F7A53E05D">2 .5 <span class="Heading">The <span class="SimpleMath">\({\mathbb Z}\)</span>-form of <span class="SimpleMath">\(U_q(\mathfrak{g})\)</span> </span></a>#X78BE3EB980F0A295">2 .6 <span class="Heading">The canonical basis </span></a>#X83BBB99685FB9FB7">2 .7 <span class="Heading"> The path model </span></a>#X7BB6B9777D54FA07">2 .8 <span class="Heading"> Notes</span></a>3 <span class="Heading">QuaGroup</span></a>#X7C202C54806653DE">3 .1 <span class="Heading">Global constants</span></a>C">3 .1 -1 QuantumField</a></span>D">3 .1 -2 _q</a></span>#X83804A6F84BB2387">3 .2 <span class="Heading">Gaussian integers</span></a>1">3 .2 -1 GaussNumber</a></span>0">3 .2 -2 GaussianFactorial</a></span>F">3 .2 -3 GaussianBinomial</a></span>#X87064F787DEA9E21">3 .3 <span class="Heading">Roots and root systems</span></a>B">3 .3 -1 RootSystem</a></span>A">3 .3 -2 BilinearFormMatNF</a></span>7">3 .3 -3 PositiveRootsNF</a></span>9">3 .3 -4 SimpleSystemNF</a></span>5">3 .3 -5 PositiveRootsInConvexOrder</a></span>D">3 .3 -6 SimpleRootsAsWeights</a></span>#X798CE6777FC473DD">3 .4 <span class="Heading">Weyl groups and their elements</span></a>4">3 .4 -1 ApplyWeylElement</a></span>4">3 .4 -2 LengthOfWeylWord</a></span>8">3 .4 -3 LongestWeylWord</a></span>9">3 .4 -4 ReducedWordIterator</a></span>A">3 .4 -5 ExchangeElement</a></span>0">3 .4 -6 GetBraidRelations</a></span>D">3 .4 -7 LongWords</a></span>#X81394E207F6AA6CF">3 .5 <span class="Heading">Quantized enveloping algebras </span></a>A">3 .5 -1 QuantizedUEA</a></span>4">3 .5 -2 ObjByExtRep</a></span>C">3 .5 -3 ExtRepOfObj</a></span>0">3 .5 -4 QuantumParameter</a></span>C">3 .5 -5 CanonicalMapping</a></span>3">3 .5 -6 WriteQEAToFile</a></span>3">3 .5 -7 ReadQEAFromFile</a></span>#X847A0459844B7A59">3 .6 <span class="Heading"> Homomorphisms and automorphisms </span></a>0">3 .6 -1 QEAHomomorphism</a></span>F">3 .6 -2 QEAAutomorphism</a></span>5">3 .6 -3 QEAAntiAutomorphism</a></span>8">3 .6 -4 AutomorphismOmega</a></span>A">3 .6 -5 AntiAutomorphismTau</a></span>0">3 .6 -6 BarAutomorphism</a></span>5">3 .6 -7 AutomorphismTalpha</a></span>D">3 .6 -8 DiagramAutomorphism</a></span>8"><code>3 .6 -9 \*</code></a></span>#X832B6D897BDBC8A3">3 .7 <span class="Heading">Hopf algebra structure</span></a>D">3 .7 -1 TensorPower</a></span>6">3 .7 -2 UseTwistedHopfStructure</a></span>7">3 .7 -3 ComultiplicationMap</a></span>F">3 .7 -4 AntipodeMap</a></span>6">3 .7 -5 CounitMap</a></span>#X8183A6857B0C3633">3 .8 <span class="Heading">Modules</span></a>1">3 .8 -1 HighestWeightModule</a></span>0">3 .8 -2 IrreducibleQuotient</a></span>9">3 .8 -3 HWModuleByTensorProduct</a></span>B">3 .8 -4 DIYModule</a></span>0">3 .8 -5 TensorProductOfAlgebraModules</a></span>2">3 .8 -6 HWModuleByGenerator</a></span>3">3 .8 -7 InducedQEAModule</a></span>6">3 .8 -8 GenericModule</a></span>C">3 .8 -9 CanonicalMapping</a></span>A">3 .8 -10 U2Module</a></span>9">3 .8 -11 MinusculeModule</a></span>0">3 .8 -12 DualAlgebraModule</a></span>4">3 .8 -13 TrivialAlgebraModule</a></span>1">3 .8 -14 WeightsAndVectors</a></span>7">3 .8 -15 HighestWeightsAndVectors</a></span>A">3 .8 -16 RMatrix</a></span>E">3 .8 -17 IsomorphismOfTensorModules</a></span>4">3 .8 -18 WriteModuleToFile</a></span>9">3 .8 -19 ReadModuleFromFile</a></span>#X83BBB99685FB9FB7">3 .9 <span class="Heading">The path model</span></a>C">3 .9 -1 DominantLSPath</a></span>F">3 .9 -2 Falpha</a></span>4">3 .9 -3 Ealpha</a></span>1">3 .9 -4 LSSequence</a></span>F">3 .9 -5 WeylWord</a></span>6">3 .9 -6 EndWeight</a></span>6">3 .9 -7 CrystalGraph</a></span>#X827A177C8416C576">3 .10 <span class="Heading"> Canonical bases </span></a>2">3 .10 -1 Falpha</a></span>9">3 .10 -2 Ealpha</a></span>1">3 .10 -3 CanonicalBasis</a></span>B">3 .10 -4 PBWElements</a></span>D">3 .10 -5 MonomialElements</a></span>4">3 .10 -6 Strings</a></span>8">3 .10 -7 PrincipalMonomial</a></span>2">3 .10 -8 StringMonomial</a></span>C">3 .10 -9 Falpha</a></span>7">3 .10 -10 Ealpha</a></span>8">3 .10 -11 CrystalBasis</a></span>2">3 .10 -12 CrystalVectors</a></span>0">3 .10 -13 Falpha</a></span>B">3 .10 -14 Ealpha</a></span>9">3 .10 -15 CrystalGraph</a></span>#X7875070C85DD4E8E">3 .11 <span class="Heading"> Universal enveloping algebras </span></a>D">3 .11 -1 UEA</a></span>E">3 .11 -2 UnderlyingLieAlgebra</a></span>F">3 .11 -3 HighestWeightModule</a></span>9">3 .11 -4 QUEAToUEAMap</a></span>iv>ml#contents">[Contents]</a> <a href="chap1_mj.html">[Next Chapter]</a> </div>/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>http://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc ">GAPDoc2HTML</a></p> Messung V0.5 in Prozent C=97 H=79 G=88
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