Higher Edu - Research dev card
Development from the higher education and research community
  • Creation or important update: 21/10/09
  • Minor correction: 22/03/10

Schur : calculator of Lie groups and symmetric function properties

This software was developed (or is under development) within the higher education and research community. Its stability can vary (see fields below) and its working state is not guaranteed.
  • Web site
  • System: UNIX-like, Windows
  • Current version: 6.05 - 24-06-2008
  • License(s): GPL
  • Status: stable release
  • Support: maintained, ongoing development
  • Designer(s): Brian G. Wybourne, the project is now managed by Franck Butelle (LIPN), Ronald C. King (University of Southampton) and Fr√©d√©ric Toumazet (LIGM).
  • Contact designer(s): franck.butelle @, frederic.toumazet @
  • Laboratory, service: LIGM, LIPN, University of Southampton, Nicholas Copernicus University


General software features

Schur is a stand alone C program for interactively calculating properties of Lie groups and symmetric functions, it has been succesfully used to solve physics problems. It can be useful for:

  • Computing Kronecker products for Lie groups and for representations of the symmetric group.
  • Computing branching rules.
  • Computing properties of irreducible representations such as dimensions, second-order Casimir and Dynkin invariants and many others.
  • Handling of direct products of several groups.
  • Computation of a wide range of properties related to symmetric functions.
  • ...
Context in which the software is used

Schur has been used to construct character tables for the Hecke algebra, to study symmetry properties for Riemann tensors and in many other problems.

Publications related to the software

J. Nzeutchap, F. Toumazet et F. Butelle. Kostka numbers and Littlewood-Richardson coefficients: distributed computation. In R.C. King, M. Bylicki and J. Karwowski (eds), Symmetry, Spectroscopy and SCHUR, Proc. Prof. Brian G. Wybourne Commemorative Meeting, Torun, Pologne , 12-­14 Juin 2005, Nicolaus Copernicus University Press, Torun, Pologne, 2006, 211-222.