An efficient algorithm computing composition factors of T(V)^⊗ n

11/12/2017

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by   Amin Saied, et al.

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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 c_λμ 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.