DeepAI AI Chat
Log In Sign Up

A new algorithm for irreducible decomposition of representations of finite groups

by   Vladimir V. Kornyak, et al.

An algorithm for irreducible decomposition of representations of finite groups over fields of characteristic zero is described. The algorithm uses the fact that the decomposition induces a partition of the invariant inner product into a complete set of mutually orthogonal projectors. By expressing the projectors through the basis elements of the centralizer ring of the representation, the problem is reduced to solving systems of quadratic equations. The current implementation of the algorithm is able to split representations of dimensions up to hundreds of thousands. Examples of calculations are given.


An Algorithm to Decompose Permutation Representations of Finite Groups: Polynomial Algebra Approach

We describe an algorithm for splitting a permutation representation of a...

An Algorithm for Computing Invariant Projectors in Representations of Wreath Products

We describe an algorithm for computing the complete set of primitive ort...

Decomposition of polynomial sets into characteristic pairs

A characteristic pair is a pair (G,C) of polynomial sets in which G is a...

Extending Snow's algorithm for computations in the finite Weyl groups

In 1990, D.Snow proposed an effective algorithm for computing the orbits...

Graded Symmetry Groups: Plane and Simple

The symmetries described by Pin groups are the result of combining a fin...

Solving Decomposable Sparse Systems

Amendola et al. proposed a method for solving systems of polynomial equa...

Square-free Strong Triangular Decomposition of Zero-dimensional Polynomial Systems

Triangular decomposition with different properties has been used for var...