Gauss Numbers
GaussNumber(n, v) : RngIntElt, RngElt -> RngElt
GaussianFactorial(n, v) : RngIntElt, RngElt -> RngElt
GaussianBinomial(n, k, v) : RngIntElt, RngIntElt, RngElt -> RngElt
Example AlgQEA_QGrpGauss (H102E1)
Construction
QuantizedUEA(R) : RootDtm -> AlgQUE
Example AlgQEA_QGrpConstr (H102E2)
AssignNames(U, S) : AlgPBW, [ MonStgElt ] ->
ChangeRing(U, R) : AlgQUE, Rng -> AlgQUE
Related Structures
CoefficientRing(U) : AlgQUE -> Fld
RootDatum(U) : AlgQUE -> RootDtm
PositiveRootsPerm(U) : AlgQUE -> SeqEnum
Example AlgQEA_QGrpRelStr (H102E3)
Operations on Elements
U ! 0 : AlgQUE, RngIntElt -> AlgQUEElt
U ! 1 : AlgQUE, RngIntElt -> AlgQUEElt
U . i : AlgQUE, RngIntElt -> AlgQUEElt
U ! r : AlgQUE, Any -> AlgQUEElt
KBinomial(U, i, s) : AlgQUE, RngIntElt, RngIntElt -> AlgQUEElt
Monomials(u) : AlgQUEElt -> SeqEnum
Coefficients(u) : AlgQUEElt -> SeqEnum
K ^ -1 : AlgQUEElt, RngIntElt -> AlgQUEElt
Degree(u, i) : AlgQUEElt, RngIntElt -> RngIntElt
KDegree(m, i) : AlgQUEElt, RngIntElt -> Tup
Example AlgQEA_QGrpEltOps (H102E4)
Representations
HighestWeightRepresentation(U, w) : AlgQUE, SeqEnum -> UserProgram
HighestWeightModule(U, w) : AlgQUE, SeqEnum -> ModTupAlg
Example AlgQEA_QGrpEltOps (H102E5)
WeightsAndVectors(V) : ModAlg -> SeqEnum, SeqEnum
HighestWeightsAndVectors(V) : ModAlg -> SeqEnum, SeqEnum
CanonicalBasis(V) : ModAlg -> SeqEnum
Example AlgQEA_CanBasMod (H102E6)
TensorProduct(Q) : SeqEnum -> ModAlg, Map
Example AlgQEA_AlgQEATP (H102E7)
Hopf Algebra Structure
UseTwistedHopfStructure(U, f, g) : AlgQUE, Map, Map ->
HasTwistedHopfStructure(U) : AlgQUE -> BoolElt, List
Counit(U) : AlgQUE -> Map
Antipode(U) : AlgQUE -> Map
Comultiplication(U, d) : AlgQUE, RngIntElt -> UserProgram
Example AlgQEA_QGrpComult (H102E8)
Automorphisms
BarAutomorphism(U) : AlgQUE -> Map
AutomorphismOmega(U) : AlgQUE -> Map
AntiAutomorphismTau(U) : AlgQUE -> Map
AutomorphismTalpha(U, k) : AlgQUE, RngIntElt -> Map
DiagramAutomorphism(U, p) : AlgQUE, GrpPermElt -> Map
Example AlgQEA_QGrpAutoms (H102E9)
Kashiwara Operators
Falpha(m, i) : AlgQUEElt, RngIntElt -> AlgQUEElt
Ealpha(m, i) : AlgQUEElt, RngIntElt -> AlgQUEElt
Example AlgQEA_QGrpAutoms (H102E10)
The Path Model
DominantLSPath(R, hw) : RootDtm, SeqEnum -> PathLS
Falpha(p, i) : PathLS, RngIntElt -> PathLS
Ealpha(p, i) : PathLS, RngIntElt -> PathLS
WeightSequence(p) : PathLS -> SeqEnum
RationalSequence(p) : PathLS -> SeqEnum
EndpointWeight(p) : PathLS -> ModTupRngElt
Shape(p) : PathLS -> ModTupRngElt
WeylWord(p) : PathLS -> SeqEnum
IsZero(p) : PathLS -> BoolElt
p1 eq p2 : PathLS, PathLS -> BoolElt
Example AlgQEA_LSPaths (H102E11)
CrystalGraph(R, hw) : RootDtm, SeqEnum -> GrphDir, SeqEnum
Example AlgQEA_CrystGrph (H102E12)
Elements of the Canonical Basis
CanonicalElements(U, w) : AlgQUE, SeqEnum -> SeqEnum
Example AlgQEA_QGrpAutoms (H102E13)
Example AlgQEA_QGrpAutoms2 (H102E14)
Homomorphisms to the Universal Enveloping Algebra
QUAToIntegralUEAMap(U) : AlgQUE -> Map
Example AlgQEA_QEAtoUEA (H102E15)
Bibliography
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Version: V2.19 of
Mon Dec 17 14:40:36 EST 2012