Schur

"Schur is a stand alone C program for interactively calculating properties of Lie groups and symmetric functions. Schur has been designed to answer questions of relevance to a wide range of problems of special interest to chemists, mathematicians and physicists - particularly for persons who need specific knowledge relating to some aspect of Lie groups or symmetric functions and yet do not wish to be encumbered with complex algorithms. The objective of Schur is to supply results with the complexity of the algorithms hidden from view so that the user can effectively use Schur as a scratch pad, obtaining a result and then using that result to derive new results in a fully interactive manner. Schur can be used as a tool for calculating branching rules, Kronecker products, Casimir invariants, dimensions, plethysms, S-function operations, Young diagrams and their hook lengths etc.

As well as being a research tool Schur forms an excellent tool for helping students to independently explore the properties of Lie groups and symmetric functions and to test their understanding by creating simple examples and moving on to more complex examples. The user has at his or her disposal over 160 commands which may be nested to give a vast variety of potential operations. Every command, with examples, is described in a 200 page manual. Attention has been given to input/output issues to simplify input and to give a well organized output. The output may be obtained in TeX form if desired. Log files may be created for subsequent editing. On line help files may be brought to screen at any time.
 
Among the many tasks amenable to Schur are the following:

• The calculation of Kronecker products for all the compact Lie groups and for the ordinary and spin representations of the symmetric group. Not only for individual irreducible representations but also lists of irreducible representations. List handling is a general feature of Schur.
• The calculation of branching rules with the ability to successively branch through a chain of nested groups.
• The calculation of the properties of irreducible representations such as dimensions, second-order Casimir and Dynkin invariants, the trace of the n-th order Casimir invariants and the conversion between partition and Dynkin labelling of irreducible representations.
• The handling of direct products of several groups.
• The computation of a wide range of properties related to Schur function operations such as the Littlewood-Richardson rule, inner products, skew products, and plethysms as well as the inclusion of commands for generating the terms in infinite series of Schur functions up to a user defined cutoff.
• The computation of the properties of the symmetric Q-functions with respect to operations such as the analogous Littlewood-Richardson rule, skew and inner products.
• The standardisation of non-standard representations of groups by the use of modification procedures.
• Calculation of properties of the classical symmetric functions.

http://schur.sourceforge.net/ 

https://sourceforge.net/projects/schur/