128 citations · 699 across the 35 of their papers we have counts for
17 papers · 1 filter
Elliptic Quantum Toroidal Algebra and Affine Quiver Gauge Theories
Hitoshi Konno, Kazuyuki Oshima
We introduce a new elliptic quantum toroidal algebra . Various representations in the quantum toroidal algebra are extended to the elli…
Elliptic Stable Envelopes and Finite-dimensional Representations of Elliptic Quantum Group
Hitoshi Konno
We construct a finite dimensional representation of the face type, i.e dynamical, elliptic quantum group associated with on the Gelfand-Tsetlin basis of the tensor product o…
Elliptic Weight Functions and Elliptic q-KZ Equation
Hitoshi Konno
By using representation theory of the elliptic quantum group U_{q,p}(sl_N^), we present a systematic method of deriving the weight functions. The resultant sl_N type elliptic weigh…
Elliptic Quantum Groups U_{q,p}(gl_N) and E_{q,p}(gl_N)
Hitoshi Konno
We reformurate a central extension of Felder's elliptic quantum group in the FRST formulation as a topological algebra E_{q,p}(gl_N) over the ring of formal power series in p. We t…
Elliptic Quantum Group U_{q,p}(B_N^{(1)}) and Vertex Operators
Hitoshi Konno, Kazuyuki Oshima
Assuming the existence of the L-operators, we study the Hopf algebroid structure of U_{q,p}(B_N^{(1)}). As an application, we derive the type I and II vertex operators, which inter…
Elliptic Algebra U_{q,p}(g^) and Quantum Z-algebras
Rasha M. Farghly, Hitoshi Konno, Kazuyuki Oshima
A new definition of the elliptic algebra U_{q,p}(g^) associated with an untwisted affine Lie algebra g^ is given as a topological algebra over the ring of formal power series in p.…
Elliptic Quantum Group U_{q,p}(\hat{sl}_2), Hopf Algebroid Structure and Elliptic Hypergeometric Series
Hitoshi Konno
We propose a new realization of the elliptic quantum group equipped with the H-Hopf algebroid structure on the basis of the elliptic algebra U_{q,p}(\hat{sl}_2). The algebra U_{q,p…
Elliptic Quantum Group U_{q,p}(\hat{sl}_2) and Vertex Operators
Hitoshi Konno
Introducing an H-Hopf algebroid structure into U_{q,p}(\widedhat{sl}_2), we investigate the vertex operators of the elliptic quantum group U_{q,p}(\widedhat{sl}_2) defined as inter…
Dynamical R Matrices of Elliptic Quantum Groups and Connection Matrices for the q-KZ Equations
Hitoshi Konno
For any affine Lie algebra , we show that any finite dimensional representation of the universal dynamical matrix of the elliptic quantum group ${\…
The Vertex-Face Correspondence and Correlation Functions of the Fusion Eight-Vertex Model I: The General Formalism
Takeo Kojima, Hitoshi Konno, Robert Weston
Based on the vertex-face correspondence, we give an algebraic analysis formulation of correlation functions of the fusion eight-vertex model in terms of the correspondi…
Fusion of Baxter's Elliptic -matrix and the Vertex-Face Correspondence
Hitoshi Konno
The matrix elements of the fusion of Baxter's elliptic -matrix, , are given explicitly. Based on a note by Jimbo, we give a formula which show that $R^…
The Vertex-Face Correspondence and the Elliptic 6j-symbols
Hitoshi Konno
A new formula connecting the elliptic -symbols and the fusion of the vertex-face intertwining vectors is given. This is based on the identification of the fusion intertwini…
The Drinfeld Realization of the Elliptic Quantum Group B_{q,lambda}(A_2^(2))
Takeo Kojima, Hitoshi Konno
We construct a realization of the L-operator satisfying the RLL-relation of the face type elliptic quantum group B_{q,lambda}(A_2^(2)). The construction is based on the elliptic an…
The Elliptic Algebra U_{q,p}(sl_N^) and the Deformation of W_N Algebra
Takeo Kojima, Hitoshi Konno
After reviewing the recent results on the Drinfeld realization of the face type elliptic quantum group B_{q,lambda}(sl_N^) by the elliptic algebra U_{q,p}(sl_N^), we investigate a…
The elliptic algebra U_{q,p}(\hat{sl}_N) and the Drinfeld realization of the elliptic quantum group B_{q,λ}(\hat{sl}_N)
Takeo Kojima, Hitoshi Konno
By using the elliptic analogue of the Drinfeld currents in the elliptic algebra U_{q,p}(\hat{sl}_N), we construct a L-operator, which satisfies the RLL-relations characterizing the…
On Lepowsky-Wilson's Z-algebra
Y. Hara, M. Jimbo, H. Konno +2
We show that the deformed Virasoro algebra specializes in a certain limit to Lepowsky-Wilson's Z-algebra. This leads to a free field realization of the affine Lie algebra \hat{sl_2…
Elliptic algebra U_{q,p}(^sl_2): Drinfeld currents and vertex operators
M. Jimbo, H. Konno, S. Odake +1
We investigate the structure of the elliptic algebra U_{q,p}(^sl_2) introduced earlier by one of the authors. Our construction is based on a new set of generating series in the qua…