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Hamiltonian interpretation of p-adic Whittaker functions

Banff International Research Station for Mathematical Innovation and Discovery

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}.

Mathematics; Number theory; Quantum theory

video/mp4

Author affiliation: University of Minnesota

2017-02-05

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60403

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/