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<div class="pcenter"><table class="chlink"><tr><td class="chlink1">Goto Chapter: </td><td><a href="chap0.html">Top</a></td><td><a href="chap1.html">1</a></td><td><a href="chap2.html">2</a></td><td><a href="chap3.html">3</a></td><td><a href="chapBib.html">Bib</a></td><td><a href="chapInd.html">Ind</a></td></tr></table><br /></div>
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<h1><strong class="pkg">QuaGroup</strong></h1>
<p>Version 1.3</p>
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<p><b>Willem A. de Graaf
</b>
<br />e-mail: <a href="mailto: degraaf@science.unitn.it"> degraaf@science.unitn.it</a>
<br />WWW: <a href="http://www.science.unitn.it/~degraaf">http://www.science.unitn.it/~degraaf</a>
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<h3>Copyright</h3>
<p>(C) 2002 Willem A. de Graaf</p>
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<h3>Contents</h3>
<a href="chap1.html#s0ss0">1. Introduction</a><br />
<a href="chap2.html#s0ss0">2. Background</a><br />
<a href="chap2.html#s1ss0">2.1 Gaussian Binomials</a><br />
<a href="chap2.html#s2ss0">2.2 Quantized enveloping algebras</a><br />
<a href="chap2.html#s3ss0">2.3 Representations of $U_q(\mathfrak{g})$ </a><br />
<a href="chap2.html#s4ss0">2.4 PBW-type bases </a><br />
<a href="chap2.html#s5ss0">2.5 The ${\mathbb Z}$-form of $U_q(\mathfrak{g})$ </a><br />
<a href="chap2.html#s6ss0">2.6 The canonical basis </a><br />
<a href="chap2.html#s7ss0">2.7 The path model </a><br />
<a href="chap2.html#s8ss0">2.8 Notes</a><br />
<a href="chap3.html#s0ss0">3. QuaGroup</a><br />
<a href="chap3.html#s1ss0">3.1 Global constants</a><br />
<a href="chap3.html#s1ss1">3.1-1 QuantumField</a><br />
<a href="chap3.html#s1ss2">3.1-2 _q</a><br />
<a href="chap3.html#s2ss0">3.2 Gaussian integers</a><br />
<a href="chap3.html#s2ss1">3.2-1 GaussNumber</a><br />
<a href="chap3.html#s2ss2">3.2-2 GaussianFactorial</a><br />
<a href="chap3.html#s2ss3">3.2-3 GaussianBinomial</a><br />
<a href="chap3.html#s3ss0">3.3 Roots and root systems</a><br />
<a href="chap3.html#s3ss1">3.3-1 RootSystem</a><br />
<a href="chap3.html#s3ss2">3.3-2 BilinearFormMatNF</a><br />
<a href="chap3.html#s3ss3">3.3-3 PositiveRootsNF</a><br />
<a href="chap3.html#s3ss4">3.3-4 SimpleSystemNF</a><br />
<a href="chap3.html#s3ss5">3.3-5 PositiveRootsInConvexOrder</a><br />
<a href="chap3.html#s3ss6">3.3-6 SimpleRootsAsWeights</a><br />
<a href="chap3.html#s4ss0">3.4 Weyl groups and their elements</a><br />
<a href="chap3.html#s4ss1">3.4-1 ApplyWeylElement</a><br />
<a href="chap3.html#s4ss2">3.4-2 LengthOfWeylWord</a><br />
<a href="chap3.html#s4ss3">3.4-3 LongestWeylWord</a><br />
<a href="chap3.html#s4ss4">3.4-4 ReducedWordIterator</a><br />
<a href="chap3.html#s4ss5">3.4-5 ExchangeElement</a><br />
<a href="chap3.html#s4ss6">3.4-6 GetBraidRelations</a><br />
<a href="chap3.html#s4ss7">3.4-7 LongWords</a><br />
<a href="chap3.html#s5ss0">3.5 Quantized enveloping algebras </a><br />
<a href="chap3.html#s5ss1">3.5-1 QuantizedUEA</a><br />
<a href="chap3.html#s5ss2">3.5-2 ObjByExtRep</a><br />
<a href="chap3.html#s5ss3">3.5-3 ExtRepOfObj</a><br />
<a href="chap3.html#s5ss4">3.5-4 QuantumParameter</a><br />
<a href="chap3.html#s5ss5">3.5-5 CanonicalMapping</a><br />
<a href="chap3.html#s5ss6">3.5-6 WriteQEAToFile</a><br />
<a href="chap3.html#s5ss7">3.5-7 ReadQEAFromFile</a><br />
<a href="chap3.html#s6ss0">3.6 Homomorphisms and automorphisms </a><br />
<a href="chap3.html#s6ss1">3.6-1 QEAHomomorphism</a><br />
<a href="chap3.html#s6ss2">3.6-2 QEAAutomorphism</a><br />
<a href="chap3.html#s6ss3">3.6-3 QEAAntiAutomorphism</a><br />
<a href="chap3.html#s6ss4">3.6-4 AutomorphismOmega</a><br />
<a href="chap3.html#s6ss5">3.6-5 AntiAutomorphismTau</a><br />
<a href="chap3.html#s6ss6">3.6-6 BarAutomorphism</a><br />
<a href="chap3.html#s6ss7">3.6-7 AutomorphismTalpha</a><br />
<a href="chap3.html#s6ss8">3.6-8 DiagramAutomorphism</a><br />
<a href="chap3.html#s6ss9">3.6-9 \*</a><br />
<a href="chap3.html#s7ss0">3.7 Hopf algebra structure</a><br />
<a href="chap3.html#s7ss1">3.7-1 TensorPower</a><br />
<a href="chap3.html#s7ss2">3.7-2 UseTwistedHopfStructure</a><br />
<a href="chap3.html#s7ss3">3.7-3 ComultiplicationMap</a><br />
<a href="chap3.html#s7ss4">3.7-4 AntipodeMap</a><br />
<a href="chap3.html#s7ss5">3.7-5 CounitMap</a><br />
<a href="chap3.html#s8ss0">3.8 Modules</a><br />
<a href="chap3.html#s8ss1">3.8-1 HighestWeightModule</a><br />
<a href="chap3.html#s8ss2">3.8-2 IrreducibleQuotient</a><br />
<a href="chap3.html#s8ss3">3.8-3 HWModuleByTensorProduct</a><br />
<a href="chap3.html#s8ss4">3.8-4 DIYModule</a><br />
<a href="chap3.html#s8ss5">3.8-5 TensorProductOfAlgebraModules</a><br />
<a href="chap3.html#s8ss6">3.8-6 HWModuleByGenerator</a><br />
<a href="chap3.html#s8ss7">3.8-7 InducedQEAModule</a><br />
<a href="chap3.html#s8ss8">3.8-8 GenericModule</a><br />
<a href="chap3.html#s8ss9">3.8-9 CanonicalMapping</a><br />
<a href="chap3.html#s8ss10">3.8-10 U2Module</a><br />
<a href="chap3.html#s8ss11">3.8-11 MinusculeModule</a><br />
<a href="chap3.html#s8ss12">3.8-12 DualAlgebraModule</a><br />
<a href="chap3.html#s8ss13">3.8-13 TrivialAlgebraModule</a><br />
<a href="chap3.html#s8ss14">3.8-14 WeightsAndVectors</a><br />
<a href="chap3.html#s8ss15">3.8-15 HighestWeightsAndVectors</a><br />
<a href="chap3.html#s8ss16">3.8-16 RMatrix</a><br />
<a href="chap3.html#s8ss17">3.8-17 IsomorphismOfTensorModules</a><br />
<a href="chap3.html#s8ss18">3.8-18 WriteModuleToFile</a><br />
<a href="chap3.html#s8ss19">3.8-19 ReadModuleFromFile</a><br />
<a href="chap3.html#s9ss0">3.9 The path model</a><br />
<a href="chap3.html#s9ss1">3.9-1 DominantLSPath</a><br />
<a href="chap3.html#s9ss2">3.9-2 Falpha</a><br />
<a href="chap3.html#s9ss3">3.9-3 Ealpha</a><br />
<a href="chap3.html#s9ss4">3.9-4 LSSequence</a><br />
<a href="chap3.html#s9ss5">3.9-5 WeylWord</a><br />
<a href="chap3.html#s9ss6">3.9-6 EndWeight</a><br />
<a href="chap3.html#s9ss7">3.9-7 CrystalGraph</a><br />
<a href="chap3.html#s10ss0">3.10 Canonical bases </a><br />
<a href="chap3.html#s10ss1">3.10-1 Falpha</a><br />
<a href="chap3.html#s10ss2">3.10-2 Ealpha</a><br />
<a href="chap3.html#s10ss3">3.10-3 CanonicalBasis</a><br />
<a href="chap3.html#s10ss4">3.10-4 PBWElements</a><br />
<a href="chap3.html#s10ss5">3.10-5 MonomialElements</a><br />
<a href="chap3.html#s10ss6">3.10-6 Strings</a><br />
<a href="chap3.html#s10ss7">3.10-7 PrincipalMonomial</a><br />
<a href="chap3.html#s10ss8">3.10-8 StringMonomial</a><br />
<a href="chap3.html#s10ss9">3.10-9 Falpha</a><br />
<a href="chap3.html#s10ss10">3.10-10 Ealpha</a><br />
<a href="chap3.html#s10ss11">3.10-11 CrystalBasis</a><br />
<a href="chap3.html#s10ss12">3.10-12 CrystalVectors</a><br />
<a href="chap3.html#s10ss13">3.10-13 Falpha</a><br />
<a href="chap3.html#s10ss14">3.10-14 Ealpha</a><br />
<a href="chap3.html#s10ss15">3.10-15 CrystalGraph</a><br />
<a href="chap3.html#s11ss0">3.11 Universal enveloping algebras </a><br />
<a href="chap3.html#s11ss1">3.11-1 UEA</a><br />
<a href="chap3.html#s11ss2">3.11-2 UnderlyingLieAlgebra</a><br />
<a href="chap3.html#s11ss3">3.11-3 HighestWeightModule</a><br />
<a href="chap3.html#s11ss4">3.11-4 QUEAToUEAMap</a><br />
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