Mathematics Colloquia and Seminars

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The LLT algorithm is a remarkable modern result on an old problem, namely computing the decomposition numbers of the symmetric groups in finite characteristic. It uses the representation theory of the quantum groups to obtain information about the Hecke Algebras at roots of unity. Despite using new and difficult machinery, the result gives a simple combinatorial way to compute the decomposition numbers of the Hecke Algebras at roots of unity. I will present a very brief explination of this result, hopefully with time to give a few examples.