# Ist product table.m

Structure coefficient tables for the associateive envelopes of su(mult) algebras.

## Syntax

    [product_table_left,product_table_right]=ist_product_table(mult)


## Description

This function returns tables of expansion coefficients of products of irreducible spherical tensors, essentially returning the coefficients defined in Equation 23 of http://dx.doi.org/10.1063/1.3398146

## Arguments

    mult      - multiplicity of the spin in question


## Returns

    product_table_left   - coefficient table for left side products

product_table_right  - coefficient table for right side products


Output contains the structure constants in the following conventions:

    T{n}*T{m}=sum_over_k[product_table_left(n,m,k)*T{k}]

T{m}*T{n}=sum_over_k[product_table_right(n,m,k)*T{k}]


Disk caching is used and updated automatically.

## Examples

This function is used by p_superop.m to build matrix representations of spin operators.

## Notes

Irreducible spherical tensors are indexed as described in Appendix_B:_spin_state_indexing. Because Matlab indexing starts from 1, the T00 spherical tensor has an index of 1.