Yasuhiko Yamada

A geometric description of the elliptic Painlevé equation (2008)

A Lax formalism for the elliptic Painlev\'e equation is presented. The construction is based on the geometry of the curves on ${\mathbb P}^1\times{\mathbb P}^1$ and described in terms of the point...

Kenji Kajiwara, Tetsu Masuda, Masatoshi Noumi, Yasuhiro Ohta, Yasuhiko Yamada

This note is an introduction to a geometric aspect of the elliptic Painlev e equation which is described as a non-autonomous deformation of the addition formula on cubic curves.

and Inhomogeneous Paths (2007)

Goro Hatayama, Anatol N. Kirillov, Masato Okado, Taichiro Takagi, Yasuhiko Yamada

Let B (l) be the perfect crystal for the l-symmetric tensor representation of the quantum affine algebra U 0 q ( b sl n). For a partition = (1; : : : ; m), elements of the tensor product B ( 1)\Omega

Singular vectors of the Virasoro algebra in terms of Jack symmetric polynomials (2007)

Katsuhisa Mimachi, Yasuhiko Yamada

We present an explicit formula of the Virasoro singular vectors in terms of Jack symmetric polynomials. The parameter t in the Virasoro central charge c = 13 \Gamma 6(t + 1=t) is just identified with...

Affine Weyl group symmetries in Painlev'e (2007)

Masatoshi Noumi, Yasuhiko Yamada

type equations

Tau functions in combinatorial Bethe ansatz (2006)

Kuniba, Atsuo, Sakamoto, Reiho, Yamada, Yasuhiko

We introduce ultradiscrete tau functions associated with rigged configurations for A^{(1)}_n. They satisfy an ultradiscrete version of the Hirota bilinear equation and play a role analogous to a...

Crystal interpretation of Kerov-Kirillov-Reshetikhin bijection (2006)

Kuniba, Atsuo, Okado, Masato, Sakamoto, Reiho, Takagi, Taichiro, Yamada, Yasuhiko

The Kerov-Kirillov-Reshetikhin (KKR) bijection is the crux in proving fermionic formulas. It is defined by a combinatorial algorithm on rigged configurations and highest paths. We reformulate the KKR...

Five-dimensional Supergravity and Hyperbolic Kac-Moody Algebra G2H (2005)

Mizoguchi, Shun'ya, Mohri, Kenji, Yamada, Yasuhiko

Motivated by the recent analysis of the E10 sigma model for the study of M theory, we study a one-dimensional sigma model associated with the hyperbolic Kac-Moody algebra G2H and its link to D=5, N=2...

Cubic Pencils and Painlevé Hamiltonians (2005)

Kajiwara, Kenji, Masuda, Tetsu, Noumi, Masatoshi, Ohta, Yasuhiro, Yamada, Yasuhiko, 梶原, 健司, ...

Kyushu University 21st Century COE Program Development of Dynamic Mathematics with High Functionality

POINT CONFIGURATIONS, CREMONA TRANSFORMATIONS AND THE ELLIPTIC DIFFERENCE PAINLEVE EQUATION (2005)

Kajiwara, Kenji, Masuda, Tetsu, Noumi, Masatoshi, Ohta, Yasuhiro, Yamada, Yasuhiko, 梶原, 健司, ...

Kyushu University 21st Century COE Program Development of Dynamic Mathematics with High Functionality

Construction of Hypergeometric Solutions to the q-Painlev\'e Equations (2005)

Kajiwara, Kenji, Masuda, Tetsu, Noumi, Masatoshi, Ohta, Yasuhiro, Yamada, Yasuhiko

Hypergeometric solutions to the q-Painlev\'e equations are constructed by direct linearization of disrcrete Riccati equations. The decoupling factors are explicitly determined so that the linear...

Construction of hypergeometric solutions to the q-Painlevé equations (2005)

Kajiwara, Kenji, Masuda, Tetsu, Noumi, Masatoshi, Ohta, Yasuhiro, Yamada, Yasuhiko, 梶原, 健司, ...

Kyushu University 21st Century COE Program Development of Dynamic Mathematics with High Functionality

A geometric description of the elliptic Painleve equation (2005)

Kajiwara, Kenji, Masuda, Tetsu, Ohta, Yasuhiro, Yamada, Yasuhiko

Box-ball system with reflecting end (2004)

Kuniba, Atsuo, Okado, Masato, Yamada, Yasuhiko

A soliton cellular automaton on a one dimensional semi-infinite lattice with a reflecting end is presented. It extends a box-ball system on an infinite lattice associated with the crystal base of...

Hypergeometric solutions to the q-Painlev\'e equations (2004)

Kajiwara, Kenji, Masuda, Tetsu, Noumi, Masatoshi, Ohta, Yasuhiro, Yamada, Yasuhiko

Hypergeometric solutions to seven q-Painlev\'e equations in Sakai's classification are constructed. Geometry of plane curves is used to reduce the q-Painlev\'e equations to the three-term recurrence...

Cubic Pencils and Painlev\'e Hamiltonians (2004)

Kajiwara, Kenji, Masuda, Tetsu, Noumi, Masatoshi, Ohta, Yasuhiro, Yamada, Yasuhiko

We present a simple heuristic method to derive the Painlev\'e differential equations from the corresponding geometry of rational surafces. We also give a direct relationship between the cubic pencils...

Hypergeometric solutions to the q-Painlevé equations (2004)

Kajiwara, Kenji, Masuda, Tetsu, Noumi, Masatoshi, Ohta, Yasuhiro, Yamada, Yasuhiko, 梶原, 健司, ...

Kyushu University 21st Century COE Program Development of Dynamic Mathematics with High Functionality

_10E_9 solution to the elliptic Painlev'e equation (2003)

Kajiwara, Kenji, Noumi, Masatoshi, Masuda, Tetsu, Ohta, Yasuhiro, Yamada, Yasuhiko

A $\tau$ function formalism for Sakai's elliptic Painlev'e equation is presented. This establishes the equivalence between the two formulations by Sakai and by Ohta-Ramani-Grammaticos. We also give a...

Tropical R and Tau Functions (2003)

Kuniba, Atsuo, Okado, Masato, Takagi, Taichiro, Yamada, Yasuhiko

Tropical R is the birational map that intertwines products of geometric crystals and satisfies the Yang-Baxter equation. We show that the D^{(1)}_n tropical R introduced by the authors and its...

Geometric Crystal and Tropical R for D^(1)_n (2002)

Kuniba, Atsuo, Okado, Masato, Takagi, Taichiro, Yamada, Yasuhiko

We construct a geometric crystal for the affine Lie algebra D^{(1)}_n in the sense of Berenstein and Kazhdan. Based on a matrix realization including a spectral parameter, we prove uniqueness and...

A new Lax pair for the sixth Painlev\'e equation associated with $\hat{\mathfrak{so}}(8)$ (2002)

Tropical Robinson-Schensted-Knuth correspondence and birational Weyl group actions (2002)

A new Lax pair for the sixth Painlev\'e equation $P_{VI}$ is constructed in the framework of the loop algebra $\mathfrak{so}(8)[z,z^{-1}]$. The whole affine Weyl group symmetry of $P_{VI}$ is...

W(E_10) Symmetry, M-Theory and Painleve Equations (2002)

By using an elementary matrix approach, based on the technique of discrete Toda equation, we construct subtraction-free rational and piecewise linear transformations associated with various...

Mizoguchi, Shun'ya, Yamada, Yasuhiko

The Weyl group symmetry W(E_k) is studied from the points of view of the E-strings, Painleve equations and U-duality. We give a simple reformulation of the elliptic Painleve equation in such a way...

q-Painlev\'e systems arising from q-KP hierarchy (2001)

Kajiwara, Kenji, Noumi, Masatoshi, Yamada, Yasuhiko

A system of q-Painlev\'e type equations with multi-time variables t_1,...,t_M is obtained as a similarity reduction of the N-reduced q-KP hierarchy. This system has affine Weyl group symmetry of type...

Discrete dynamical systems with $W(A^{(1)}_{m-1} \times A^{(1)}_{n-1})$ symmetry (2001)

Kajiwara, Kenji, Noumi, Masatoshi, Yamada, Yasuhiko

We give a birational realization of affine Weyl group of type $A^{(1)}_{m-1} \times A^{(1)}_{n-1}$. We apply this representation to construct some discrete integrable systems and discrete Painlev\'e...

A study on the fourth q-Painlev\'e equation (2000)

Kajiwara, Kenji, Noumi, Masatoshi, Yamada, Yasuhiko

A q-difference analogue of the fourth Painlev\'e equation is proposed. Its symmetry structure and some particular solutions are investigated.

Birational Weyl group action arising from a nilpotent Poisson algebra (2000)

Mordell-Weil Lattice via String Junctions (1999)

We propose a general method to realize an arbitrary Weyl group of Kac-Moody type as a group of birational canonical transformations, by means of a nilpotent Poisson algebra. We also give a Lie...

Fukae, Mitsuaki, Yamada, Yasuhiko, Yang, Sung-Kil

We analyze the structure of singularities, Mordell-Weil lattices and torsions of a rational elliptic surface using string junctions in the background of 12 7-branes. The classification of the...

Energy Functions in Box Ball Systems (1999)

Fukuda, Kaori, Okado, Masato, Yamada, Yasuhiko

The box ball system is studied in the crystal theory formulation. New conserved quantities and the phase shift of the soliton scattering are obtained by considering the energy function (or...

Determinant Formulas for the Toda and Discrete Toda Equations (1999)

Kajiwara, Kenji, Masuda, Tetsu, Noumi, Masatoshi, Ohta, Yasuhiro, Yamada, Yasuhiko

Determinant formulas for the general solutions of the Toda and discrete Toda equations are presented. Application to the $\tau$ functions for the Painlev\'e equations is also discussed.

Affine 7-brane Backgrounds and Five-Dimensional $E_N$ Theories on $S^1$ (1999)

Yamada, Yasuhiko, Yang, Sung-Kil

Elliptic curves for the 7-brane configurations realizing the affine Lie algebras $\wh E_n$ $(1 \leq n \leq 8)$ and $\wh{\wt E}_n$ $(n=0,1)$ are systematically derived from the cubic equation for a...

Symmetries in the fourth Painlevé equation and Okamoto polynomials (1999)

Determinant formulas for the {$\tau$}-functions of the Painlevé equations of type {$A$} (1999)

The fourth Painlev\'e equation $P_{IV}$ is known to have symmetry of the affine Weyl group of type $A^{(1)}_2$ with respect to the Bäcklund transformations. We introduce a new representation of...

Remarks on Fermionic Formula (1998)

Explicit determinant formulas are presented for the $\tau$-functions of the generalized Painlevé equations of type $A$. This result allows an interpretation of the $\tau$-functions as the Plücker...

Hatayama, Goro, Kuniba, Atsuo, Okado, Masato, Takagi, Taichiro, Yamada, Yasuhiko

Fermionic formulae originate in the Bethe ansatz in solvable lattice models. They are specific expressions of some q-polynomials as sums of products of q-binomial coefficients. We consider the...

Determinant formulas for the $\tau$-functions of the Painlev\'e equations of type $A$ (1998)

Higher order Painlev\'e equations of type $A^{(1)}_l$ (1998)

Explicit determinant formulas are presented for the $\tau$ functions of the generalized Painlev\'e equations of type $A$. This result allows an interpretation of the $\tau$-functions as the Pl\"ucker...

Affine Weyl groups, discrete dynamical systems and Painleve equations (1998)

A series of systems of nonlinear equations with affine Weyl group symmetry of type $A^{(1)}_l$ is studied. This series gives a generalization of Painlev\'e equations $P_{IV}$ and $P_{V}$ to higher...

Character Formulae of $\hat{sl}_n$-Modules and Inhomogeneous Paths (1998)

A new class of representations of affine Weyl groups on rational functions are constructed, in order to formulate discrete dynamical systems associated with affine root systems. As an application,...

Hatayama, Goro, Kirillov, Anatol N., Kuniba, Atsuo, Okado, Masato, Takagi, Taichiro, Yamada, Yasuhiko

Let B_{(l)} be the perfect crystal for the l-symmetric tensor representation of the quantum affine algebra U'_q(\hat{sl(n)}). For a partition mu = (mu_1,...,mu_m), elements of the tensor product...

Symmetries in the fourth Painleve equation and Okamoto polynomials (1997)

On $q$-Clebsch Gordan Rules and the Spinon Character Formulas for Affine $C_2^{(1)}$ Algebra (1997)

We propose a new representation of the fourth Painlev\'e equation in which the $A^{(1)}_2$-symmetries become clearly visible. By means of this representation, we clarify the internal relation between...

Kostka polynomials and energy functions in solvable lattice models (1997)

A $q$-analog of the Clebsch Gordan rules for the tensor products of the fundamental representations of Yangian is introduced. Its relation to the crystal base theory and application to the spinon...

Atsushi Nakayashiki, Yasuhiko Yamada

The relation between the charge of Lascoux-Schuzenberger and the energy function in solvable lattice models is clarified. As an application, A.N.Kirillov's conjecture on the expression of the...

Symmetries in the fourth Painlevé equation and Okamoto polynomials (1997)

Masatoshi Noumi, Yasuhiko Yamada

this paper we propose a new representation of the fourth Painlev'e equation in which the A

Crystallizing the spinon basis (1996)

Kostka Polynomials and Energy Functions in Solvable Lattice Models (1995)

Crystalline Spinon Basis for RSOS Models (1995)

The relation between the charge of Lascoux-Schuzenberger and the energy function in solvable lattice models is clarified. As an application, A.N.Kirillov's conjecture on the expression of the...

Crystalizing the Spinon Basis (1995)

The crystalline spinon basis for the RSOS models associated with $\widehat{sl_2}$ is studied. This basis gives fermionic type character formulas for the branching coefficients of the coset...

Singular vectors of the Virasoro algebra in terms of Jack symmetric polynomials (1995)

The quasi-particle structure of the higher spin XXZ model is studied. We obtained a new description of crystals associated with the level $k$ integrable highest weight $U_q(\widehat{sl_2})$ modules...

Mimachi, Katsuhisa, Yamada, Yasuhiko

The mirror symmetry-a historical introduction (1993)

The mirror symmetry-a historical introduction (1993)

The mirror symmetry-a historical introduction (1993)