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      Metaplectic Iwahori Whittaker functions and supersymmetric lattice models

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          Abstract

          In this paper we consider Iwahori Whittaker functions on n-fold metaplectic covers ˜G of G(F) with G a split reductive group over a non-archimedean local field F. For every element ϕ of a basis of Iwahori Whittaker functions, and for every g˜G, we evaluate ϕ(g) by recurrence relations over the Weyl group using "vector Demazure-Whittaker operators." Specializing to the case of G=GLr, we exhibit a solvable lattice model whose partition function equals ϕ(g). These models are of a new type associated with the quantum affine super group Uq(^gl(r|n)). The recurrence relations on the representation theory side then correspond to solutions to Yang-Baxter equations for the lattice models.

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          Author and article information

          Journal
          31 December 2020
          Article
          2012.15778
          a6e7039e-4082-4590-b251-d15822882f01

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          Custom metadata
          22E50, 82B23, 16T25, 05E05, 17B37, 11F70
          math.RT math.NT math.QA

          Number theory,Algebra
          Number theory, Algebra

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