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Documentation of MARTY
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Documentation of MARTY
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Exceptional semi-simple Lie algebra F4. More...
#include <semiSimpleAlgebra.h>
Public Member Functions | |
| F4 () | |
| Default constructor. | |
| ~F4 () | |
| Destructor. | |
| algebra::Type | getType () const override |
| Pure virtual function overriden in derived classes. More... | |
| void | setCartanMatrix () override |
| Pure virtual function overriden in derived classes. Initializes the Cartan matrix specifically to the given semi-simple Lie algebra. | |
| void | setSquaredNorm () override |
| Pure virtual function overriden in derived classes. Initializes norms of simple roots specifically to the given semi-simple Lie algebra. | |
| mty::Irrep | getDefiningRep () const override |
 Public Member Functions inherited from mty::SemiSimpleAlgebra | |
| SemiSimpleAlgebra (int t_l) | |
| Constructor with one parameter. More... | |
| virtual | ~SemiSimpleAlgebra () |
| Destructor. | |
| csl::Expr | getQuadraticCasimir (const AlgebraState &irrep) const |
| Returns the expression (symbolic, rational number) of the quadratic Casimir operator for a representation. More... | |
| virtual csl::Expr | getIndex (const Irrep &irrep, size_t n) const |
| virtual Irrep | highestWeightRep (const AlgebraState &highestWeight, bool mult=true) const |
| Calculates and returns the highest weight representation. Determines all states with their multiplicities and returns the corresponding Irrep object. Overriden in R algebra. More... | |
| virtual Irrep | highestWeightRep (const std::vector< int > &highestWeight, bool mult=true) const |
| Calculates and returns the highest weight representation. Determines all states with their multiplicities and returns the corresponding Irrep object. Overriden in R algebra. More... | |
| virtual Irrep | getTrivialRep () const |
| Returns the trivial representation of the algebra. Overriden in R algebra. More... | |
| virtual SumIrrep | tensorProduct (const Irrep &A, const Irrep &B, bool mult=true) const |
| Calculates and returns the product of two Irrep in the algebra. The result is decomposed in a sum of irreducible representations, stored in a SumIrrep. Overriden in the R algebra. More... | |
| virtual SumIrrep | tensorProduct (const SumIrrep &A, const Irrep &B, bool mult=true) const |
| virtual SumIrrep | tensorProduct (const Irrep &A, const SumIrrep &B, bool mult=true) const |
| SumIrrep | tensorProduct (const SumIrrep &A, const SumIrrep &B, bool mult=true) const |
| virtual void | sortRep (std::vector< AlgebraState > &rep, std::vector< int > &mult) const |
| Sorts by modifing input paramaters a set of AlgebraState with their multiplicities. One state is considered "bigger" than another if the sum of its dinkin labels is bigger. Overriden in the R algebra. More... | |
| int | getOrderL () const |
| Returns the order of the algebra, i.e. the number of simple roots l. More... | |
Additional Inherited Members | |
| Protected Member Functions inherited from mty::SemiSimpleAlgebra | |
| void | init () |
| Initialization function called in derived classes to initialize the cartan matrix, the Weyl group and the norms of simple roots. | |
| virtual csl::Expr | getEta () const |
| Protected Attributes inherited from mty::SemiSimpleAlgebra | |
| const int | l |
| Order of the semi-simple algebra, i.e. number of simple roots. | |
| std::vector< int > | rho |
| std::vector of size l. Particular root (half-sum of simple roots) useful in calculations. More... | |
| csl::vector_expr | absoluteNorms |
| Absolute norms of simple roots used in the computation of the quadratic Casimir operator. See SemiSimpleAlgebra::getQuadraticCasimir(). | |
| std::vector< int > | squaredNorm |
| std::vector of integers of size l. Contains squared norms of all simple roots. | |
| std::vector< std::vector< int > > | positiveRoots |
| Contains all positive roots in a std::vector. Each positive root is a std::vector of integers of size l: dinkin labels in co-root space. | |
| std::vector< std::vector< int > > | cartanMatrix |
| Cartan matrix of the algebra. | |
| std::vector< std::vector< int > > | rootMetric |
| Metric for roots in co-root space, i.e. metrix to apply in order to compute scalar dot between roots expressed with their dinkin labels. | |
| csl::Expr | symbolicRho |
| Symbolic version of the half-sum of simple roots (see positiveRoots). Contains the factor 1/2 that positiveRoots does not. | |
| csl::Expr | symbolicCartan |
| Symbolic version of the cartan matrix. | |
| csl::Expr | inverseCartan |
| Inverse cartan matrix. | |
| csl::Expr | symbolicMetric |
| Symbolic metric in root space. i.e. different from rootMetric that is the metric in co-root space. | |
| csl::vector_expr | symbolicRoots |
| Symbolic version of positiveRoots, each root is a csl::Vector of csl::Integer in co-root space (dinkin labels). | |
| csl::vector_expr | symbolicSquaredNorms |
| Symbolic version of squaredNorm. | |
| std::vector< std::pair< AlgebraState, Irrep > > | irreps |
| std::vector< IndexData > | indices |
Exceptional semi-simple Lie algebra F4.
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overridevirtual |
Pure virtual function overriden in derived classes.
Implements mty::SemiSimpleAlgebra.
1.8.13