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Metaplectic Whittaker functions and the Yang-Baxter equation Bump, Daniel


In 2012, Brubaker, Bump, Friedberg, Chinta and Gunnells proposed statistical-mechanical models for p-adic Whittaker functions on the degree $n$ metaplectic cover of $\hbox{GL}(r)$. In recent work of Brubaker, Buciumas and Bump, the corresponding Yang-Baxter equations have been found. The corresponding quantum group is identified as a Drinfeld twist of $U_q(\widehat{\mathfrak{gl}}(n))$. The effect of the Drinfeld twisting is to introduce Gauss sums into the R-matrix. The scattering matrix of the intertwining operators on the (nonunique) Whittaker models, previously studied by Kazhdan-Patterson and Chinta-Gunnells, is thus reinterpreted as the R-matrix of this quantum group. Moreover, the internal states of these generalized ice-type models (which are not visible to the intertwining operator) are built up by tensoring from $(n+1)$-dimensional supersymmetric modules for the quantum affine Lie superalgebra $U_q(\widehat{gl}(n|1))$.

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