#### Filter Results:

#### Publication Year

1991

2015

#### Publication Type

#### Co-author

#### Publication Venue

#### Key Phrases

Learn More

- Michio Jimbo, Hitoshi Konno, Satoru Odake, Jun Ichi, Shiraishi
- 1997

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)

- H Awata, Y Matsuo, S Odake, J Shiraishi
- 1994

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)

- Jun ichi Shiraishi, Harunobu Kubo, Hidetoshi Awata, Satoru Odake
- 1995

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.

- Hidetoshi Awata, Yutaka Matsuo, Satoru Odake, Jun
- 1995

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)

- Satoru Odake, Ryu Sasaki
- 2004

We show that the equilibrium positions of the Ruijsenaars-Schneider-van Diejen systems with the trigonometric potential are given by the zeros of the Askey-Wilson polynomials with five parameters. The corresponding single particle quantum version, which is a typical example of " discrete " quantum mechanical systems with a q-shift type kinetic term, is… (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)

- Satoru Odake, Ryu Sasaki
- 2004

Shape invariance is an important ingredient of many exactly solvable quantum mechanics. Several examples of shape invariant " discrete quantum mechanical systems " are introduced and discussed in some detail. They arise in the problem of describing the equilibrium positions of Ruijsenaars-Schneider type systems, which are " discrete " counterparts of… (More)

- Satoru Odake, Ryu Sasaki
- 2008

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)

- Hidetoshi Awata, Masafumi Fukuma, Yutaka Matsuo, Satoru Odake
- 1995

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)