6 papers · 1 filter
The Bethe Equation at q=0, The M"obius Inversion Formula, and Weight Multiplicities: III. The X^{(r)}_N case
A. Kuniba, T. Nakanishi, Z. Tsuboi
It is shown that the numbers of off-diagonal solutions to the U_q(X^{(r)}_N) Bethe equation at q=0 coincide with the coefficients in the recently introduced canonical power series…
Scattering rules in soliton cellular automata associated with crystal bases
G. Hatayama, A. Kuniba, M. Okado +2
Solvable vertex models in a ferromagnetic regime give rise to soliton cellular automata at q=0. By means of the crystal base theory, we study a class of such automata associated wi…
Combinatorial R matrices for a family of crystals : C^{(1)}_n and A^{(2)}_{2n-1} cases
Goro Hatayama, Atsuo Kuniba, Masato Okado +1
The combinatorial R matrices are obtained for a family {B_l} of crystals for U'_q(C^{(1)}_n) and U'_q(A^{(2)}_{2n-1}), where B_l is the crystal of the irreducible module correspond…
Bethe Equation at q=0, Möbius Inversion Formula, and Weight Multiplicities: I. sl(2) case
Atsuo Kuniba, Tomoki Nakanishi
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 express…
Finite Crystals and Paths
Goro Hatayama, Yoshiyuki Koga, Atsuo Kuniba +2
We consider a category of finite crystals of a quantum affine algebra whose objects are not necessarily perfect, and set of paths, semi-infinite tensor product of an object of this…
Remarks on Fermionic Formula
Goro Hatayama, Atsuo Kuniba, Masato Okado +2
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…