An efficient algorithm computing composition factors of $T(V)^{\otimes n}$
Data Structures and Algorithms
2017-11-15 v1
Abstract
We present an algorithm that computes the composition factors of the n-th tensor power of the free associative algebra on a vector space. The composition factors admit a description in terms of certain coefficients determining their irreducible structure. By reinterpreting these coefficients as counting the number of ways to solve certain `decomposition-puzzles' we are able to design an efficient algorithm extending the range of computation by a factor of over 750. Furthermore, by visualising the data appropriately, we gain insights into the nature of the coefficients leading to the development of a new representation theoretic framework called PD-modules.
Cite
@article{arxiv.1711.04326,
title = {An efficient algorithm computing composition factors of $T(V)^{\otimes n}$},
author = {Amin Saied},
journal= {arXiv preprint arXiv:1711.04326},
year = {2017}
}