BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Hamiltonian interpretation of p-adic Whittaker functions Brubaker, Benjamin


Whittaker functions on $p$-adic groups are expressible as partition functions of six-vertex models on a rectangular lattice; at least, this is known for Cartan types $A$ and $B$ and expected more generally. We show that, in type $A$, this may alternately be viewed as the discrete time evolution of a one-dimensional system of free fermions. The Hamiltonian dictating the evolution arises from the Lie superalgebra $\mathfrak{gl}(1 | 1)$ and the Whittaker function may thus be viewed as a kind of generalized ``tau function'' in the terminology of the Kyoto school. All of these notions from statistical mechanics will be explained in the talk and illustrated with pictures. This is joint work with A. Schultz based on {\tt arXiv:1606.00020}.

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