# Graphical Tensor Product Reduction for so(5)

## Input Values for Multiplets:

Introduction

When describing physical systems with Lie algebras it is vital to reduce tensor products of irreducible representations into sums of such representations. The graphical tensor product reduction scheme of J. P. Antoine and D. Speiser provides an algorithm to calculate these sums, without engaging in long and tedious calculations. Given two representations one wants to couple, the first one is placed into this landscape of irreducible representations (shown below), centered at the second multiplet. Taking into account the parity of the various sectors of the landscape and the multiplicities of the first multiplet one can easily calculate even high-dimensional tensor products.
Further information can be found in here.

Input Values

In order to perform a tensor product reduction one needs to specify the two multiplets, by specifying the p-value (sidelength along the diagonal) and the q-value (sidelength along the horizontal) of both multiplets (p1,q1,p2,q2). These two input values characterize a multiplet of so(5) uniquely and are displayed below the landscape of so(5). If invalid values are typed in, the program evaluates them as "0". Since high dimensional calculations require a big landscape and a tremendous amount of calculation (for example the calculation of (20,20) ⊗ (20,20) takes about one 30 seconds), the biggest multiplet one can create (and couple) is (20,20) .
The landscape is programmed in such a way that one can explore the landscape by using "drag and drop": Going to far out of the landscape leads to the user being set back to the origin of the landscape.

Concluding we wish a lot of fun with the program and hope to encourage people to inform themselves about this particular tensor product reduction scheme.

Greetings Bühlmann Patrick

Input

1. Multiplet = = 2. Multiplet = =

Solution

=