A Discrete Analogue of Periodic Delta Bose Gas and Affine Hecke Algebra
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We consider an eigenvalue problem for a discrete analogue of the Hamiltonian of the non-ideal Bose gas with delta-potentials on a circle. It is a two-parameter deformation of the discrete Hamiltonian for joint moments of the partition function of the O'Connell-Yor semi-discrete polymer. We construct the propagation operator by using integral-reflection operators, which give a representation of the affine Hecke algebra. We also construct eigenfunctions by means of the Bethe ansatz method. In the case where one parameter of our Hamiltonian is equal to zero, the eigenfunctions are given by specializations of the Hall-Littlewood polynomials.
- Funkcialaj Ekvacioj
Funkcialaj Ekvacioj 57(1), 107-118, 2014
Division of Functional Equations, The Mathematical Society of Japan