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Littlemann Paths: an interface between representations of semi simple Lie algebras and probabilistic study of functions on the set of walks on lattices

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If you have a question about this talk, please contact Elena Yudovina.

The theory of crystals and specifically that of Littlemann paths on the weight lattices associated to semi simple Lie algebras has one particular fact that might be of interest to probabilists: crystals partition the set of paths. Lie theorists like crystals because they carry most, perhaps all, the information about representations of the Lie algebras.

I would like to explain what I mean by this. This might be of use to probabilists if their interest is in a function on the set of walks on a lattice whose expected value over a given crystal is particularly easy to work out. Examples of such easy functions arise naturally from representation theory.

This talk is part of the Statistical Laboratory Graduate Seminars series.

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