Mathematics Colloquia and Seminars

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Crystal graphs are labeled, directed graphs that combinatorially model the representations of Lie (super)algebras. Given an abstract crystal graph, can one recognize whether or not it is a crystal graph of such representations? This is the problem of characterization for crystals of the Lie (super)algebra. In the case where the associated Lie algebra has a simply laced-root system, Stembridge provided a characterization using a set of local axioms. In joint work with Maria Gillespie, Graham Hawkes and Anne Schilling, we developed and proved a characterization of crystal graphs for the queer Lie superalgebra, $\mathfrak{q}(n+1)$. I will also show a brief computer demonstration on how SageMath aided the development of this characterization.