157 citations · 353 across the 9 of their papers we have counts for
9 papers
Non-Stationary Difference Equation and Affine Laumon Space II: Quantum Knizhnik-Zamolodchikov Equation
Hidetoshi Awata, Koji Hasegawa, Hiroaki Kanno +4
We show that Shakirov's non-stationary difference equation, when it is truncated, implies the quantum Knizhnik-Zamolodchikov (-KZ) equation for $U_{\mathsf v}\bigl(A_1^{(1)}\big…
Non-Stationary Difference Equation and Affine Laumon Space: Quantization of Discrete Painlevé Equation
Hidetoshi Awata, Koji Hasegawa, Hiroaki Kanno +4
We show the relation of the non-stationary difference equation proposed by one of the authors and the quantized discrete Painlevé VI equation. The five-dimensional Seiberg-Witten c…
Periodic ILW equation with discrete Laplacian
J. Shiraishi, Y. Tutiya
We study an integro-differential equation which generalizes the periodic intermediate long wave (ILW) equation. The kernel of the singular integral involved is an elliptic function…
Quasi-Hopf twistors for elliptic quantum groups
M. Jimbo, H. Konno, S. Odake +1
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 bee…
Virasoro-type Symmetries in Solvable Models
H. Awata, H. Kubo, S. Odake +1
Virasoro-type symmetries and their roles in solvable models are reviewed. These symmetries are described by the two-parameter Virasoro-type algebra by choosing the para…
Quantum Deformation of the W_N Algebra
H. Awata, H. Kubo, S. Odake +1
We review the W_N algebra and its quantum deformation, based on free field realizations. The (quantum deformed) W_N algebra is defined through the (quantum deformed) Miura transfor…
Quantum Algebras and Macdonald Polynomials
H. Awata, H. Kubo, S. Odake +1
We derive a quantum deformation of the algebra and its quantum Miura transformation, whose singular vectors realize the Macdonald polynomials.
A Note on Calogero-Sutherland Model, W_n Singular Vectors and Generalized Matrix Models
H. Awata, Y. Matsuo, S. Odake +1
We review some recent results on the Calogero-Sutherland model with emphasis upon its algebraic aspects. We give integral formulae for excited states (Jack polynomials) of this mod…
Collective fields, Calogero-Sutherland model and generalized matrix models
H. Awata, Y. Matsuo, S. Odake +1
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 func…