Mathematica program for computations in representation theory of affine and finite-dimensional Lie algebras.

This program is based on the properties of weight system and uses Weyl symmetry. Central problems are weight multiplicity calculation, branching of representation to representation of subalgebras and tensor product decomposition. For more detail see doc/paper.pdf.

Mathematica. Tested with versions 7 and 8 on Linux and Windows. More details in doc/paper.pdf

git clone git://github.com/naa/Affine.git

Add path to the beginning of your notebook

AppendTo[$Path,"src/"]; <<affine.m;

The demonstration notebook demo.nb is in the folder demo. Notebook paper.nb in the same folder contains the code which was used to produce examples in the paper.

All public functions of the package has online help, which can be invoked this way:

?functionName

For more details see files demo/demo.nb,demo/paper.nb and doc/paper.pdf.

Unit tests are in file tests/tests.m. To run all the tests just read the contents of this file into your notebook after adding the folder to $Path with

<<tests.m

This separate module implements Kirillov-Reshetikhin formula for the graded and usual tensor product decomposition of simple Lie algebra modules. This module can be used independently from the affine.m. The only needed input is the Cartan matrix of Lie algebra.

Add path to the beginning of your notebook

AppendTo[$Path,"src/"];

<<affine.m; (* Optional *)

<<kirillov-reshetikhin.m;

And use as follows:

gradedTensorProductMultiplicity[{0,3},{{0,0},{3,0}},{{2,-1},{-1,2}}]

or

a2=makeSimpleRootSystem[A,2];

Expand[Simplify[{#,gradedTensorProductMultiplicity[#,{{8,0}},cartanMatrix[a2]]}&/@dynkinLabels[a2]/@Flatten[weightSystem[a2][weight[a2][8,0]]]]]

Online demo