78 citations · 265 across the 23 of their papers we have counts for
25 papers
Classification of marked elliptic root systems with non-reduced affine quotient
A. Fialowski, K. Iohara, Y. Saito
The class of root systems, called elliptic root systems, were introduced in 1985 by K. Saito, for his studies on a normal surface singularity which contains a regular elliptic curv…
Classification of simple strong Harish-Chandra -modules
Yuly Billig, Vyacheslav Futorny, Kenji Iohara +1
We classify all simple strong Harish-Chandra modules for the Lie superalgebra . We show that every such module is either strongly cuspidal or a module of the highest weight…
On Lie algebras of generalized Jacobi matrices
Alice Fialowski, Kenji Iohara
In this lecutre note, we consider infinite dimensional Lie algebras of generalized Jacobi matrices and , which are important in soliton…
Maurice Janet's algorithms on systems of linear partial differential equations
Kenji Iohara, Philippe Malbos
This article presents the emergence of formal methods in theory of partial differential equations (PDE) in the french school of mathematics through Janet's work in the period 1913-…
Invariants of the Weyl Group of Type
Kenji Iohara, Yosihisa Saito
In this note, we show the polynomiality of the ring of invariants with respect to the Weyl group of type .
Schur-Weyl duality for certain infinite dimensional -modules
Kenji Iohara, Gus Lehrer, Ruibin Zhang
Let be the two-dimensional simple module and be a projective Verma module for the quantum group of at generic . We show that for any , the endo…
Classification of Simple Cuspidal Modules over a Lattice Lie Algebra of Witt type
Yuly Billig, Kenji Iohara
Let be the lattice Lie algebra of Witt type associated with an additive inclusion with . In this article, the classificati…
Homology of Lie Algebras of Orthogonal and Symplectic Generalized Jacobi Matrices
Alice Fialowski, Kenji Iohara
In this note, we compute the homology with trivial coefficients of Lie algebras of generalized Jacobi matrices of type and over an associative unital -algebra with $k…
From analytical mechanical problems to rewriting theory through M. Janet
Kenji Iohara, Philippe Malbos
This note surveys the historical background of the Gröbner basis theory for D-modules and linear rewriting theory. The objective is to present a deep interaction of these two field…
Homology of the Lie algebra
A. Fialowski, K. Iohara
In this note we compute the homology of the Lie algebra where is an associative unital -algebra which is used in higher dimensional soliton theory.…
Singular Degenerations of Lie Supergroups of Type
Kenji Iohara, Fabio Gavarini
The complex Lie superalgebras of type - also denoted by - are usually considered for "non-singular" values of the parameter ,…
Temperley-Lieb at roots of unity, a fusion category and the Jones quotient
K. Iohara, G. I. Lehrer, R. B. Zhang
When the parameter is a root of unity, the Temperley-Lieb algebra is non-semisimple for almost all . In this work, using cellular methods, we give explicit generat…
The Jones quotients of the Temperley-Lieb algebras
K. Iohara, G. I. Lehrer, R. B. Zhang
When the parameter is a root of unity, the Temperley-Lieb algebra is non-semisimple for almost all . Jones showed that there is a canonical symmetric bilinear form…
A Global version of Grozman's theorem
Kenji Iohara, Olivier Mathieu
Let X be a manifold. The classification of all equivariant bilinear maps between tensor density modules over X has been investigated by Yu Grozman, who has provided a full classifi…
Classification of Simple Lie Algebras on a Lattice
Kenji Iohara, Olivier Mathieu
Let be a lattice of rank . A Lie algebra on the lattice is a Lie algebra such that for all . In this articl…
Hirota bilinear forms with 2-toroidal symmetry
K. Iohara, Y. Saito, M. Wakimoto
In this note, we compute Hirota bilinear forms arising from both homogeneous and principal realization of vertex representations of 2-toroidal Lie algebras of type .
Generalization and Deformation of Drinfeld quantum affine algebras
Jintai Ding, Kenji Iohara
Drinfeld gave a current realization of the quantum affine algebras as a Hopf algebra with a simple comultiplication for the quantum current operators. In this paper, we will presen…
Drinfeld comultiplication and vertex operators
Jintai Ding, Kenji Iohara
For the current realization of the quantum affine algebras, Drinfeld gave a simple comultiplication of the quantum current operators. With this comultiplication, we study the relat…
Bosonic representations of Yangian Double $\cD Y_{\hbar}(\gtg)$ with $\gtg=\gtgl_N,\gtsl_N$
Kenji Iohara
On the basis of `' formalism, we introduce the quantum double of the Yangian $Y_{\hbar}(\gtg)$ for $\gtg=\gtgl_N,\gtsl_N$ with a central extension. The Gauss decomposition…
A central extension of $\cD Y_{\hbar}(\gtgl_2)$ and its vertex representations
Kenji Iohara, Mika Kohno
A central extension of $\cD Y_{\hbar}(\gtgl_2)$ is proposed. The bosonization of level module and vertex operators are also given.
Notes on highest weight modules of the elliptic algebra
O. Foda, K. Iohara, M. Jimbo +3
We discuss a construction of highest weight modules for the recently defined elliptic algebra , and make several conjectures concerning them. The mo…
An elliptic quantum algebra for
Omar Foda, K. Iohara, M. Jimbo +3
An elliptic deformation of is proposed. Our presentation of the algebra is based on the relation , where and are eight-vertex -matrices wit…
Solutions to Knizhnik-Zamolodchikov equations with coefficients in non-bounded modules
Kenji Iohara, Feodor Malikov
We explicitly write dowm integral formulas for solutions to Knizhnik-Zamolodchikov equations with coefficients in non-bounded -- neither highest nor lowest weight -- $\gtsl_{n+1}$-…
Rings of skew polynomials and Gel'fand-Kirillov conjecture for quantum groups
Kenji Iohara, Feodor Malikov
We introduce and study action of quantum groups on skew polynomial rings and related rings of quotients. This leads to a ``q-deformation'' of the Gel'fand-Kirillov conjecture which…