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Creators/Authors contains: "Kedem, Rinat"

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  1. ; ; ; ; (, Letters in Mathematical Physics)
    Abstract We give a description of the Hallnäs–Ruijsenaars eigenfunctions of the 2-particle hyperbolic Ruijsenaars system as matrix coefficients for the order 4 element$$S\in SL(2,{\mathbb {Z}})$$ S ∈ S L ( 2 , Z ) acting on the Hilbert space ofGL(2) quantum Teichmüller theory on the punctured torus. TheGL(2) Macdonald polynomials are then obtained as special values of the analytic continuation of these matrix coefficients. The main tool used in the proof is the cluster structure on the moduli space of framedGL(2)-local systems on the punctured torus, and an$$SL(2,{\mathbb {Z}})$$ S L ( 2 , Z ) -equivariant embedding of theGL(2) spherical DAHA into the quantized coordinate ring of the corresponding cluster Poisson variety. 
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  2. ; (, Selecta Mathematica)
    Full Text Available 
  3. ; (, Representation Theory, Mathematical Physics, and Integrable Systems)
    Alexeev, A.; Frenkel, E.; Rosso, M.; Webster, B.; Yakimov, M. (Ed.)
    We propose solutions of the quantum Q-systems of types BN,CN,DN in terms of q-difference operators, generalizing our previous construction for the Q- system of type A. The difference operators are interpreted as q-Whittaker limits of discrete time evolutions of Macdonald-van Diejen type operators. We conjecture that these new operators act as raising and lowering operators for q-Whittaker functions, which are special cases of graded characters of fusion products of KR- modules. 
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    Accepted Manuscript Full Text Available