TiledArray  0.7.0
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TiledArray::Irrep Class Reference

Irrep of an $ S_n $ symmetric group. More...

#include <irrep.h>

Public Member Functions

 Irrep ()=delete
 
 Irrep (Irrep &&)=default
 
 ~Irrep ()=default
 
Irrep & operator= (Irrep &&)=default
 
 Irrep (const Irrep &other)
 
 Irrep (const std::initializer_list< unsigned int > &mu, const std::initializer_list< unsigned int > &M)
 Irrep constructor. More...
 
Irrep & operator= (const Irrep &other)
 Copy operator. More...
 
unsigned int degree () const
 Irrep degree accessor. More...
 
const unsigned int * data () const
 Data accessor. More...
 

Detailed Description

Irrep of an $ S_n $ symmetric group.

The data is represented using Yamanouchi symbol, $ M $ , which is a row of $ n $ numbers $ M_i $ $ (i = 0, \dots , n-1) $, where $ M_i $ is the number of the row in the standard Young tableau, counting from above, in which the number $ i $ appears. For example, the standard irreps for the $ S_3 $ group are:

\[ \begin{tabular}{ c c c } Young tableaux & partition [$\mu$] & Yamanouchi symbols M \\ & & \\ \begin{tabular}{ |c| } \hline 1 \\ \hline 2 \\ \hline 3 \\ \hline \end{tabular} & [111] & 123 \\ & & \\ \begin{tabular}{ |c|c|c| } \hline 1 & 2 & 3 \\ \hline \end{tabular} & [3] & 111 \\ & & \\ \begin{tabular}{ |c|c } \hline 1 & \multicolumn{1}{|c|}{2} \\ \hline 3 \\ \cline{1-1} \end{tabular} & [21] & 112 \\ & & \\ \begin{tabular}{ |c|c } \hline 1 & \multicolumn{1}{|c|}{3} \\ \hline 2 \\ \cline{1-1} \end{tabular} & [21] & 121 \\ \end{tabular} \]

To construct an irrep, you must provide the partition for the Young tableaux and the Yamanouchi symbols as follows:

Irrep S3_irrep({1,1,1}, {1,2,3});

Definition at line 76 of file irrep.h.

Constructor & Destructor Documentation

◆ Irrep() [1/4]

TiledArray::Irrep::Irrep ( )
delete

◆ Irrep() [2/4]

TiledArray::Irrep::Irrep ( Irrep &&  )
default

◆ ~Irrep()

TiledArray::Irrep::~Irrep ( )
default

◆ Irrep() [3/4]

TiledArray::Irrep::Irrep ( const Irrep &  other)
inline

Definition at line 90 of file irrep.h.

◆ Irrep() [4/4]

TiledArray::Irrep::Irrep ( const std::initializer_list< unsigned int > &  mu,
const std::initializer_list< unsigned int > &  M 
)
inline

Irrep constructor.

Definition at line 98 of file irrep.h.

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Member Function Documentation

◆ data()

const unsigned int* TiledArray::Irrep::data ( ) const
inline

Data accessor.

Returns
A const pointer to the partition and symbol data.
Note
The size of the data array is 2 * degree.

Definition at line 157 of file irrep.h.

◆ degree()

unsigned int TiledArray::Irrep::degree ( ) const
inline

Irrep degree accessor.

Returns
The degree of the symmetry group to which this irrep belongs

Definition at line 151 of file irrep.h.

◆ operator=() [1/2]

Irrep& TiledArray::Irrep::operator= ( Irrep &&  )
default

◆ operator=() [2/2]

Irrep& TiledArray::Irrep::operator= ( const Irrep &  other)
inline

Copy operator.

Parameters
otherThe irrep to be copied
Returns
A reference to this irrep

Definition at line 138 of file irrep.h.

The documentation for this class was generated from the following file: