Representation Theory
Magma computes ordinary and modular representations of finite groups - character tables, Brauer characters, decomposition matrices, and induction/restriction. Meataxe algorithms identify irreducible constituents.
Contributors
A substantial package for working with basic algebras has been contributed by Jon Carlson (Athens, Ga.). The package provides a wide range of facilities including automorphism group and cohomology.
A database of basic algebras for the p-modular group algebras of some of the smaller groups appearing in the ATLAS of Finite Groups has been constructed by Jon Carlson (Athens, Ga.). A similar library contains the basic algebras of a small collection of Schur algebras S(n,r).
The algorithm of John Dixon for constructing the ordinary irreducible representation of a finite group from its character has been implemented by Derek Holt (Warwick).
Derek Holt (Warwick) has made a number of important contributions to the design of the module theory algorithms employed in Magma.
An algorithm of Sam Conlon for determining the degrees of the ordinary irreducible characters of a soluble group (without determining the full character table) has been implemented by Derek Holt (Warwick).
In 2011, Derek Holt (Warwick) and John Cannon (Magma) developed a package for computing the projective indecomposable KG-modules for a finite group G.
A number of intrinsics for working with various aspects of KG-modules, K a field, have been implemented by Derek Holt (Warwick). Among many others these include functions for module extensions and bimodules.
The algorithms used in Magma for finding the lattice of submodules and the endomorphism ring of a KG-module (K a finite field) were developed by Charles Leedham-Green (QMW, London) and Allan Steel (Magma).