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We give a recursive method for computing all values of a basis of Iwahori Whittaker functions on a split reductive group G over a nonarchimedean local field F using an action of the Hecke algebra. Then we specialize to G = GL r where we show that there exists a family of solvable lattice models whose partition functions give precisely these values. 'Solvability' of the model means there is a family of Yang-Baxter equations which imply, among other things, that these partition functions satisfy the same recursion as the Iwahori Whittaker functions. The R-matrices for these Yang-Baxter equations come from a Drinfeld twist of the quantum affine Lie superalgebra U q ( gl(r|1)), and are connected to the standard intertwining operators on the unramified principal series.The lattice models we consider are similar to (but still different from) models introduced by Borodin and Wheeler. We explore relationships between our models and theirs, and between the partition functions and nonsymmetric Macdonald polynomials.

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 = GL r , 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 U q ( 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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We present a new formulation of the tensionless string (T = 0) where the space-time conformal symmetry is manifest. Using a Hamiltonian BRST scheme we quantize this Conformal String and find that it has critical dimension D = 2. This is in keeping with our classical result that the model describes massless particles in this dimension. It is also consistent with our previous results which indicate that quantized conformally symmetric tensionless strings describe a topological phase away from D = 2.We reach our result by demanding nilpotency of the BRST charge and consistency with the Jacobi identities. The derivation is presented in two different ways: in operator language and using mode expansions.Careful attention is payed to regularization, a crucial ingredient in our calculations.