Abstract

Kashiwara operators partition the space of walks on lattices into crystals. Appealing consequences of this fact include the expected value of nice functions on paths conditioned on a crystal is the trace of a corresponding differential operator in a representation corresponding to that crystal and the definition of the actions of the Kashiwara operators on paths fits well with the uncertainty principle. I will describe Kashiwara operators with particular reference to sl_2 and sl_3, and explore how concepts useful in physics, such as action, path integral and normal ordering might be interpreted in the context of Kashiwara operators.