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Crystal bases, probability measures on path spaces, variations on the theme of path integrals for quantum mechanics.

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Kashiwara operators are at the heart of crystal bases for quantised enveloping algebras. As operators acting on the space of paths on a lattice, they partition the space of paths into highly symmetric subsets. Defining a measure on the sigma algebra offers an alternative approach to path integration, distinct from but related to the usual approach.

This is the second talk in the Empty Room Seminar Series – a very informal series in which new ideas can be tried out on a blackboard. Real live audients are welcome, of course.

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