Topic guides

This section explains and analyses some key concepts that appear in RepLAB. The aim of the guides given here is not to show how to do something specific with the library, but rather to explain some notions at the heart of RepLAB and how the library works.

• Membrane vibration modes
  • Eigenvalue problem of a vibrating square membrane, part 1
  • Eigenvalue problem of a vibrating square membrane, part 2
• Symmetric SDPs
  • Preparation
  • Introduction
  • Formulating a symmetric SDP
  • Constructing a symmetric SDP matrix with additional structure
  • Imposing symmetry to an existing SDP matrix
  • Block-diagonalizing a symmetric SDP matrix
  • Comparison with a direct formulation

To go further

Specific usages of RepLAB in the field of quantum theory and quantum information are presented in the dedicated Quantum website.

Here are also some books and scientific articles presenting in more depth additional topics.

• “RepLAB: a computational/numerical approach to representation theory” presents a concise overview of the approach used by RepLAB

• “Certifying Numerical Decompositions of Compact Group Representations” presents how RepLAB’s numerical decompositions can be certified

• An introduction to representation theory: Linear Representations of Finite Groups by Jean-Pierre Serre