semiSimpleAlgebra.h File Reference

Semi simple Lie algebras: calculations of highest weight representations, products and sums of representations. More...

#include <vector>
#include <algorithm>
#include <iostream>
#include <initializer_list>
#include <string>
#include <csl.h>
#include "algebraState.h"

Go to the source code of this file.

Data Structures
struct	mty::IndexData
class	mty::SemiSimpleAlgebra
	Abstract base class for all semi-simple Lie algebras. More...
class	mty::algebra::R
	Algebra (R, +) of the U(1) group. More...
class	mty::algebra::A
	Semi-simple Lie algebra A(l) == su(l+1). More...
class	mty::algebra::B
	Semi-simple Lie algebra B(l) == so(2l+1). More...
class	mty::algebra::C
	Semi-simple Lie algebra C(l) == sp(2l). More...
class	mty::algebra::D
	Semi-simple Lie algebra D(l) == so(2l). More...
class	mty::algebra::E6
	Exceptional semi-simple Lie algebra E6. More...
class	mty::algebra::E7
	Exceptional semi-simple Lie algebra E7. More...
class	mty::algebra::E8
	Exceptional semi-simple Lie algebra E8. More...
class	mty::algebra::F4
	Exceptional semi-simple Lie algebra F4. More...
class	mty::algebra::G2
	Exceptional semi-simple Lie algebra G2. More...

Namespaces
	mty
	Namespace of MARTY.
	mty::algebra
	Enumeration of types of semi simple Lie algebras. The names being very small, we use a namespace to avoid conflicts.

Enumerations
enum	mty::algebra::Type {   mty::algebra::Type::R,   mty::algebra::Type::A,   mty::algebra::Type::B,   mty::algebra::Type::C,   mty::algebra::Type::D,   mty::algebra::Type::E6,   mty::algebra::Type::E7,   mty::algebra::Type::E8,   mty::algebra::Type::F4,   mty::algebra::Type::G2 }
	Different types of semi-simple Lie algebras. More...

Functions
std::ostream &	mty::algebra::operator<< (std::ostream &fout, mty::algebra::Type obj)
	Overload of operator<< for algebra::Type. Allows to display a string corresponding to the type of algebra instead of an integer. More...
int	mty::getCoxeterNumber (algebra::Type type, int l=0)
template<typename T >
std::ostream &	operator<< (std::ostream &fout, const std::vector< T > &vec)
template<typename T >
int	findInVector (const std::vector< T > &v, const T &element)
template<typename T >
int	binaryFindInVector (const std::vector< T > &v, const T &element)
template<typename T >
bool	addCarefully (std::vector< T > &vec, T element)
template<typename T >
std::vector< T >	operator+ (const std::vector< T > &x, const std::vector< T > &y)
template<typename T >
std::vector< T >	operator- (const std::vector< T > &x, const std::vector< T > &y)
template<typename T >
std::vector< T >	operator- (const std::vector< T > &x)
template<typename T >
std::vector< T >	operator* (T a, const std::vector< T > &x)
template<typename T >
std::vector< T >	operator* (const std::vector< T > &x, T a)
template<typename T >
T	operator* (const std::vector< T > &x, const std::vector< T > &y)
template<typename T >
std::vector< T >	operator* (const std::vector< std::vector< T >> &A, const std::vector< T > &x)
template<typename T >
std::vector< T >	operator* (const std::vector< T > &x, const std::vector< std::vector< T >> &A)
template<typename T >
std::vector< std::vector< T > >	operator* (const std::vector< std::vector< T >> &A, const std::vector< std::vector< T >> &B)

Detailed Description

Semi simple Lie algebras: calculations of highest weight representations, products and sums of representations.

Author

Gregoire Uhlrich

Version

1.3

Handles all semi-simple Lie algebras, including the exceptionnal ones ( \( E_6 \), \( E_7 \), \( E_8 \), \( F_4 \), \( G_2 \)). For more technical details see the manual that explains more deeply some concepts and gives references.