Schur is a standalone 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 interest to chemists, mathematicians, computer scientists,...
- 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 Irreductible Representation but also lists of IR.
- calculation of branching rules with the ability to successively branch through a chain of nested groups.
- calculation of the properties of IR 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 IR.
- 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.
- computation of the properties of the symmetric Q-functions with respect to operations such as the analogous Littlewood-Richardson rule, skew and inner products.
Nice and simple.