The first version of this package was released in V2.29 (October 2025). It has been developed further in each subsequent release, and is still under development. We encourage users to send feedback regarding the package, and desirable features or improvements.
The package contains implementations of certain representations of groups on free modules of finite rank, where the groups are not assumed to be finite or even finitely generated. The actions are assumed to be on the left (V is a left G-module). The goal is to be able to construct representations of reductive groups. The primary focus is on orthogonal and unitary groups.
The main purposes of the current functionality are to serve as a basis for algebraic modular forms.
Let G be a group, let R be a commutative ring, and let V be a left R[G]-module. Then V is called a representation of G. This chapter describes function available in Magma for computations concerning such representations.
The Magma category for group representations is ModRed, while elements in these spaces have type ModRedElt. Morphisms between group representations are linear maps which are compatible with the group action, and have type ModRedHom.
The representations are built on a catgeory of combinatorial free modules, whose Magma type is CombFreeMod, while elements in such modules have type CombFreeModElt.