Solvable lattice models and representations of p-adic groups
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Abstract: Solvable lattice models are statistical mechanical systems that can be
studied exactly by a method of Baxter, based on the Yang-Baxter
equation. This can be understood in terms of quantum groups. Recently
particular examples showing symmetry with respect to the Lie quantum
super group U_q(\widehat{\mathfrak{gl}}(r|n) arose in two very different
contexts: the representation theory of p-adic groups, where such models
were used by Brubaker, Buciumas, Bump and Gustafsson to study Iwahori
Whittaker functions on metaplectic groups; and in integrable
probability, in work recent of Aggarwal, Borodin and Wheeler. We will
introduce the topic starting with Baxter's work on six vertex model,
then look at more recent work explaining some of the ideas.
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