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| | A (int t_l) |
| | Constructor with one parameter. More...
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| ~A () |
| | Destructor.
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| algebra::Type | getType () const override |
| | Pure virtual function overriden in derived classes. More...
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void | setCartanMatrix () override |
| | Pure virtual function overriden in derived classes. Initializes the Cartan matrix specifically to the given semi-simple Lie algebra.
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void | setSquaredNorm () override |
| | Pure virtual function overriden in derived classes. Initializes norms of simple roots specifically to the given semi-simple Lie algebra.
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csl::Expr | getEta () const override |
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mty::Irrep | getDefiningRep () const override |
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| | SemiSimpleAlgebra (int t_l) |
| | Constructor with one parameter. More...
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virtual | ~SemiSimpleAlgebra () |
| | Destructor.
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| csl::Expr | getQuadraticCasimir (const AlgebraState &irrep) const |
| | Returns the expression (symbolic, rational number) of the quadratic Casimir operator for a representation. More...
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virtual csl::Expr | getIndex (const Irrep &irrep, size_t n) const |
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| 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...
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| 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...
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| virtual Irrep | getTrivialRep () const |
| | Returns the trivial representation of the algebra. Overriden in R algebra. More...
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| 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...
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virtual SumIrrep | tensorProduct (const SumIrrep &A, const Irrep &B, bool mult=true) const |
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virtual SumIrrep | tensorProduct (const Irrep &A, const SumIrrep &B, bool mult=true) const |
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SumIrrep | tensorProduct (const SumIrrep &A, const SumIrrep &B, bool mult=true) const |
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| 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...
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| int | getOrderL () const |
| | Returns the order of the algebra, i.e. the number of simple roots l. More...
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void | init () |
| | Initialization function called in derived classes to initialize the cartan matrix, the Weyl group and the norms of simple roots.
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const int | l |
| | Order of the semi-simple algebra, i.e. number of simple roots.
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| std::vector< int > | rho |
| | std::vector of size l. Particular root (half-sum of simple roots) useful in calculations. More...
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csl::vector_expr | absoluteNorms |
| | Absolute norms of simple roots used in the computation of the quadratic Casimir operator. See SemiSimpleAlgebra::getQuadraticCasimir().
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std::vector< int > | squaredNorm |
| | std::vector of integers of size l. Contains squared norms of all simple roots.
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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.
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std::vector< std::vector< int > > | cartanMatrix |
| | Cartan matrix of the algebra.
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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.
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csl::Expr | symbolicRho |
| | Symbolic version of the half-sum of simple roots (see positiveRoots). Contains the factor 1/2 that positiveRoots does not.
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csl::Expr | symbolicCartan |
| | Symbolic version of the cartan matrix.
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csl::Expr | inverseCartan |
| | Inverse cartan matrix.
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csl::Expr | symbolicMetric |
| | Symbolic metric in root space. i.e. different from rootMetric that is the metric in co-root space.
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csl::vector_expr | symbolicRoots |
| | Symbolic version of positiveRoots, each root is a csl::Vector of csl::Integer in co-root space (dinkin labels).
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csl::vector_expr | symbolicSquaredNorms |
| | Symbolic version of squaredNorm.
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std::vector< std::pair< AlgebraState, Irrep > > | irreps |
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std::vector< IndexData > | indices |
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Semi-simple Lie algebra A(l) == su(l+1).
Public Member Functions inherited from mty::SemiSimpleAlgebra
1.8.13