Irreducible Tensor Products over Alternating Groups

Irreducible Tensor Products over Alternating Groups

Groups Acting on Tensor Products

Groups preserving a distributive product are encountered often in algebra. Examples include automorphism groups of associative and nonassociative rings, classical groups, and automorphism groups of p-groups. While the great variety of such products precludes any realistic hope of describing the general structure of the groups that preserve them, it is reasonable to expect that insight may be ga...

Unique Decomposition of Tensor Products of Irreducible Representations of Simple Algebraic Groups

We show that a tensor product of irreducible, finite dimensional representations of a simple Lie algebra over a field of characteristic zero, determines the individual constituents uniquely. This is analogous to the uniqueness of prime factorisation of natural numbers.

Representations of the Alternating Group Which Are Irreducible over Subgroups

Recognising Tensor Products of Matrix Groups

As a contribution to the project for recognising matrix groups deened over nite elds, we describe an algorithm for deciding whether or not the natural module for such a matrix group can be decomposed into a non-trivial tensor product. In the aarmative case, a tensor decomposition is returned. As one component, we develop algorithms to compute p-local subgroups of a matrix group.