Satoru Odake

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The Yang-Baxter equation admits two classes of elliptic solutions, the vertex type and the face type. On the basis of these solutions, two types of elliptic quantum groups have been introduced (Foda et al.[1], Felder [2]). Frønsdal [3, 4] made a penetrating observation that both of them are quasi-Hopf algebras, obtained by twisting the standard quantum(More)
On the basis of the collective field method, we analyze the Calogero– Sutherland model (CSM) and the Selberg–Aomoto integral, which defines , in particular case, the partition function of the matrix models. Vertex operator realizations for some of the eigenstates (the Jack polynomials) of the CSM Hamiltonian are obtained. We derive Vira-soro constraint for(More)
A quantum deformation of the Virasoro algebra is defined. The Kac determinants at arbitrary levels are conjectured. We construct a bosonic realization of the quantum deformed Virasoro algebra. Singular vectors are expressed by the Macdonald symmetric functions. This is proved by constructing screening currents acting on the bosonic Fock space.
Using the collective field method, we find a relation between the Jack symmetric polynomials, which describe the excited states of the Calogero-Sutherland model, and the singular vectors of the W N algebra. Based on this relation, we obtain their integral representations. We also give a direct algebraic method which leads to the same result, and integral(More)
Integrability and supersymmetry of the supersymmetric extension of the sine-Gordon theory on a half-line are examined and the boundary potential which preserves both the integrability and supersymmetry on the bulk is derived. It appears that unlike the boundary bosonic sine-Gordon theory, integrability and supersymmetry strongly restrict the form and(More)
The Ruijsenaars-Schneider systems are 'discrete' version of the Calogero-Moser (CM) systems in the sense that the momentum operator p appears in the Hamiltonians as a polynomial in e ±β ′ p (β ′ is a deformation parameter) instead of an ordinary polynomial in p in the hierarchies of CM systems. We determine the polynomials describing the equilibrium(More)
Various examples of exactly solvable 'discrete' quantum mechanics are explored explicitly with emphasis on shape invariance, Heisenberg operator solutions, annihilation-creation operators, the dynamical symmetry algebras and coherent states. The eigen-functions are the (q-)Askey-scheme of hypergeometric orthogonal polynomials satisfying difference equation(More)
We propose a series of new subalgebras of the W 1+∞ algebra parametrized by polynomials p(w), and study their quasifinite representations. We also investigate the relation between such subalgebras and thê gl(∞) algebra. As an example, we investigate the W ∞ algebra which corresponds to the case p(w) = w, presenting its free field realizations and Kac(More)