Dilogarithm identities for conformal field theories and cluster algebras: simply laced case (2009)
The dilogarithm identities for the central charges of conformal field theories of simply laced type were conjectured by Bazhanov, Kirillov, and Reshetikhin. Their functional generalizations were...
T-systems and Y-systems for quantum affinizations of quantum Kac-Moody algebras (2009)
Kuniba, Atsuo, Nakanishi, Tomoki, Suzuki, Junji
The T-systems and Y-systems are classes of algebraic relations originally associated with quantum affine algebras and Yangians. Recently the T-systems were generalized to quantum affinizations of a...
Periodicities of T-systems and Y-systems (2008)
Inoue, Rei, Iyama, Osamu, Kuniba, Atsuo, Nakanishi, Tomoki, Suzuki, Junji
The unrestricted T-system is a family of relations in the Grothendieck ring of the category of the finite-dimensional modules of the Yangian or the quantum affine algebra associated with a complex...
On Frenkel-Mukhin algorithm for q-character of quantum affine algebras (2008)
Nakai, Wakako, Nakanishi, Tomoki
The q-character is a strong tool to study finite-dimensional representations of quantum affine algebras. However, the explicit formula of the q-character of a given representation has not been known...
Anatol N. Kirillov, Atsuo Kuniba, Tomoki Nakanishi
Abstract. The spectral decomposition of the path space of the vertex model associated to the vector representation of the quantized affine algebra U q ( b sl n) is studied. We give a one-to-one...
NAKAI, Wakako, NAKANISHI, Tomoki, 中西, 知樹
2000 Mathematics Subject Classification: 17B37; 05E15
Wakako Nakai, Tomoki Nakanishi
We study the Jacobi-Trudi-type determinant which is conjectured to be the $q$-character of a certain, in many cases irreducible, finite-dimensional representation of the quantum affine algebra of...
Nakai, Wakako, Nakanishi, Tomoki
We study the Jacobi-Trudi-type determinant which is conjectured to be the q-character of a certain, in many cases irreducible, finite-dimensional representation of the quantum affine algebra of type...
Nakai, Wakako, Nakanishi, Tomoki
We study the Jacobi-Trudi-type determinant which is conjectured to be the q-character of a certain, in many cases irreducible, finite-dimensional representation of the quantum affine algebra of type...
Paths, tableaux and q-characters of quantum affine algebras: the Cn case (2006)
Nakai, Wakako, Nakanishi, Tomoki
For the quantum affine algebra Uq (ˆg) with g of classical type, let χλ/μ,a be the Jacobi–Trudi-type determinant for the generating series of the (supposed) q-characters of the fundamental...
Paths, tableaux, and q-characters of quantum affine algebras: the C_n case (2005)
Nakai, Wakako, Nakanishi, Tomoki
For the quantum affine algebra $U_q(\hat{\mathfrak{g}})$ with $\mathfrak{g}$ of classical type, let $\chi_{\lambda/\mu,a}$ be the Jacobi-Trudi type determinant for the generating series of the...
KUNIBA, ATSUO, NAKANISHI, TOMOKI, TSUBOI, ZENGO
It is shown that the numbers of off-diagonal solutions to the Uq(X(r)N ) Bethe equation at q = 0 coincide with the coefficients in the recently introduced canonical power series solution of the...
The canonical solutions of the Q-systems and the Kirillov-Reshetikhin conjecture (2002)
KUNIBA, ATSUO, NAKANISHI, TOMOKI, TSUBOI, ZENGO
We study a class of systems of functional equations closely related to various kinds of integrable statistical and quantum mechanical models. We call them the finite and infinite Q-systems according...
Bethe Equation at q=0, Moebius Inversion Formula, and Weight Multiplicities: II. X_n case (2002)
KUNIBA, ATSUO, NAKANISHI, TOMOKI
We study a family of power series characterized by a system of recursion relations (Q-system) with a certain convergence property. We show that the coefficients of the series are expressed by the...
The canonical solutions of the Q-systems and the Kirillov-Reshetikhin conjecture (2001)
Kuniba, Atsuo, Nakanishi, Tomoki, Tsuboi, Zengo
We study a class of systems of functional equations closely related to various kinds of integrable statistical and quantum mechanical models. We call them the finite and infinite Q-systems according...
Bethe Equation at q=0, Moebius Inversion Formula, and Weight Multiplicities: II. X_n case (2000)
Kuniba, Atsuo, Nakanishi, Tomoki
We study a family of power series characterized by a system of recursion relations (Q-system) with a certain convergence property. We show that the coefficients of the series are expressed by the...
Bethe Equation at q=0, Möbius Inversion Formula, and Weight Multiplicities: I. sl(2) case (2000)
Kuniba, Atsuo, Nakanishi, Tomoki
The Uq(ˆsl(2)) Bethe equation is studied at q = 0. A linear congruence equation is proposed related to the string solutions. The number of its off-diagonal solutions is expressed in terms of an...
Bethe Equation at q=0, M\"obius Inversion Formula, and Weight Multiplicities: I. sl(2) case (1999)
Kuniba, Atsuo, Nakanishi, Tomoki
The U_q(\hat{sl}(2)) Bethe equation is studied at q=0. A linear congruence equation is proposed related to the string solutions. The number of its off-diagonal solutions is expressed in terms of an...
Kirillov, Anatol N., Kuniba, Atsuo, Nakanishi, Tomoki
The spectral decomposition of the path space of the vertex model associated to the level $l$ representation of the quantized affine algebra $U_q(\hat{sl}_n)$ is studied. The spectrum and its...
Skew Young diagram method in spectral decomposition of integrable lattice models (1997)
Anatol N. Kirillov, Atsuo Kuniba, Tomoki Nakanishi
Abstract. The spectral decomposition of the path space of the vertex model associated to the level l representation of the quantized affine algebra U q ( b sl n) is studied. The spectrum and its...
Skew Young diagram method in spectral decomposition of integrable lattice models (1996)
Kirillov, Anatol N., Kuniba, Atsuo, Nakanishi, Tomoki
The spectral decomposition of the path space of the vertex model associated to the vector representation of the quantized affine algebra $U_q(\hat{sl}_n)$ is studied. We give a one-to-one...
Spectral decomposition of path space in solvable lattice model (1996)
Arakawa, Tomoyuki, Nakanishi, Tomoki, Oshima, Kazuyuki, Tsuchiya, Akihiro
Spectral Decomposition of Path Space in Solvable Lattice Model (1995)
Arakawa, Tomoyuki, Nakanishi, Tomoki, Oshima, Kazuyuki, Tsuchiya, Akihiro
We give the {\it spectral decomposition} of the path space of the $U_q(\hatsl)$ vertex model with respect to the local energy functions. The result suggests the hidden Yangian module structure on the...
Fusion, mass, and representation theory of the Yangian algebra (1994)
Based on the formulation of Drinfel'd, Chari, and Pressley, a technique to analyze the structure of tensor products of the Yangian algebra representations is presented. We then apply the results to...
Functional Relations in Solvable Lattice Models II (1993)
Kuniba, Atsuo, Nakanishi, Tomoki, Suzuki, Junji
Reported are two applications of the functional relations ($T$-system) among a commuting family of row-to-row transfer matrices proposed in the previous paper Part I. For a general simple Lie algebra...
Spectra in Conformal Field Theories from the Rogers Dilogarithm (1992)
Kuniba, Atsuo, Nakanishi, Tomoki
We propose a system of functional relations having a universal form connected to the $U_q(X^{(1)}_r)$ Bethe ansatz equation. Based on the analysis of it, we conjecture a new sum formula for the...