Publications (33)
Free Boson Representation of
H. Awata, S. Odake, J. Shiraishi
A representation of the quantum affine algebra of an arbitrary level is constructed in the Fock module of eight boson fields. This realization reduces t…
Free Boson Realization of
H. Awata, S. Odake, J. Shiraishi
We construct a realization of the quantum affine algebra of an arbitrary level in terms of free boson fields. In the limit this reali…
Subalgebras of and Their Quasifinite Representations
H. Awata, M. Fukuma, Y. Matsuo +1
We propose a series of new subalgebras of the algebra parametrized by polynomials , and study their quasifinite representations. We also investigate the relati…
Anomaly in RTT relation for DIM algebra and network matrix models
H. Awata, H. Kanno, A. Mironov +4
We discuss the recent proposal of arXiv:1608.05351 about generalization of the RTT relation to network matrix models. We show that the RTT relation in these models is modified by a…
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…
Representation Theory of The Algebra
H. Awata, M. Fukuma, Y. Matsuo +1
We review the recent development in the representation theory of the algebra. The topics that we concern are, Quasifinite representation, Free field realizations, (S…
Shiraishi functor and non-Kerov deformation of Macdonald polynomials
H. Awata, H. Kanno, A. Mironov +1
We suggest a further generalization of the hypergeometric-like series due to M. Noumi and J. Shiraishi by substituting the Pochhammer symbol with a nearly arbitrary function. Moreo…
Can tangle calculus be applicable to hyperpolynomials?
H. Awata, H. Kanno, A. Mironov +1
We make a new attempt at the recently suggested program to express knot polynomials through topological vertices, which can be considered as a possible approach to the tangle calcu…
Determinant and Character of W-infinity algebra
H. Awata, M. Fukuma, Y. Matsuo +1
We diagonalize the Hilbert space of some subclass of the quasifinite module of the \Winf algebra. States are classified according to their eigenvalues for infinitely many commuting…
Excited States of Calogero-Sutherland Model and Singular Vectors of the Algebra
H. Awata, Y. Matsuo, S. Odake +1
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 v…
Tachyon Condensation and Graviton Production in Matrix Theory
H. Awata, S. Hirano, Y. Hyakutake
We study a membrane -- anti-membrane system in Matrix theory. It in fact exhibits the tachyon instability. By suitably representing this configuration, we obtain a (2+1)-dimensiona…
The MacMahon R-matrix
H. Awata, H. Kanno, A. Mironov +3
We introduce an -matrix acting on the tensor product of MacMahon representations of Ding-Iohara-Miki (DIM) algebra . This -matri…
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…
Elliptic lift of the Shiraishi function as a non-stationary double-elliptic function
H. Awata, H. Kanno, A. Mironov +1
As a development of arXiv:1912.12897, we note that the ordinary Shiraishi functions have an insufficient number of parameters to describe generic eigenfunctions of double elliptic…
Notes on Ding-Iohara algebra and AGT conjecture
H. Awata, B. Feigin, A. Hoshino +3
We study the representation theory of the Ding-Iohara algebra $\calU$ to find -analogues of the Alday-Gaiotto-Tachikawa (AGT) relations. We introduce the endomorphism o…
Quantum Algebraic Approach to Refined Topological Vertex
H. Awata, B. Feigin, J. Shiraishi
We establish the equivalence between the refined topological vertex of Iqbal-Kozcaz-Vafa and a certain representation theory of the quantum algebra of type W_{1+infty} introduced b…
Vertex Operators of the -Virasoro Algebra; Defining Relations, Adjoint Actions and Four Point Functions
H. Awata, H. Kubo, Y. Morita +2
Primary fields of the -deformed Virasoro algebra are constructed. Commutation relations among the primary fields are studied. Adjoint actions of the deformed Virasoro current on…
On complete solution of the quantum Dell system
H. Awata, H. Kanno, A. Mironov +1
The mother functions for the eigenfunctions of the Koroteev-Shakirov version of quantum double-elliptic (Dell) Hamiltonians can be presented as infinite series in Miwa variables, v…
Quasifinite Highest Weight Modules over Super Algebra
H. Awata, M. Fukuma, Y. Matsuo +1
We study quasifinite highest weight modules over the supersymmetric extension of the algebra on the basis of the analysis by Kac and Radul. We find that the quasifin…
A quantum deformation of the superconformal algebra
H. Awata, K. Harada, H. Kanno +1
We introduce a unital associative algebra , having and as complex parameters, generated by the elements (), ($m\in \m…
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…
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.
Determinant Formulae of Quasi-Finite Representation of W_{1+\infty} Algebra at Lower Levels
H. Awata, M. Fukuma, Y. Matsuo +1
We calculate the Kac determinant for the quasi-finite representation of \Winf algebra up to level 8. It vanishes only when the central charge is integer. We give an algebraic const…
Comments on the Problem of a Covariant Formulation of Matrix Theory
H. Awata, D. Minic
A possible avenue towards the covariant formulation of the bosonic Matrix Theory is explored. The approach is guided by the known covariant description of the bosonic membrane. We…
-KZ equations for quantum toroidal algebra and Nekrasov partition functions on ALE spaces
H. Awata, H. Kanno, A. Mironov +3
We describe the general strategy for lifting the Wess-Zumino-Witten model from the level of one-loop Kac-Moody to generic quantum toroidal algebras.…
Heisenberg realization for U_q(sln) on the flag manifold
H. Awata, M. Noumi, S. Odake
We give the Heisenberg realization for the quantum algebra , which is written by the -difference operator on the flag manifold. We construct it from the action of $U_…
Eigensystem and Full Character Formula of the W_{1+infinity} Algebra with c=1
H. Awata, M. Fukuma, S. Odake +1
By using the free field realizations, we analyze the representation theory of the W_{1+infinity} algebra with c=1. The eigenvectors for the Cartan subalgebra of W_{1+infinity} are…
Fusion Rules for the q-deformed Vertex Operators of U_q(sl(2)^)
H. Awata, Y. Yamada
We analyze the properties of the q-vertex operators of U_q(sl(2)^) introduced by Frenkel and Reshetikhin. As the condition for the null vector decoupling, we derive the existence c…
q-Difference Realization of U_q(sl(M|N)) and Its Application to Free Boson Realization of U_q(\widehat{sl}(2|1))
H. Awata, S. Odake, J. Shiraishi
We present a q-difference realization of the quantum superalgebra U_q(sl(M|N)), which includes Grassmann even and odd coordinates and their derivatives. Based on this result we obt…
A non-torus link from topological vertex
H. Awata, H. Kanno, A. Mironov +2
The recently suggested tangle calculus for knot polynomials is intimately related to topological string considerations and can help to build the HOMFLY-PT invariants from the topol…
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…
Many-body Dynamics of D0--Branes
H. Awata, S. Chaudhuri, M. Li +1
We show that the growth of the size with the number of partons holds in a Thomas-Fermi analysis of the threshold bound state of D0--branes. Our results sharpen the evidence that fo…
Collective Field Description of Spin Calogero-Sutherland Models
H. Awata, Y. Matsuo, T. Yamamoto
Using the collective field technique, we give the description of the spin Calogero-Sutherland Model (CSM) in terms of free bosons. This approach can be applicable for arbitrary cou…