Difference L operators and a Casorati determinant solution to the T-system for twisted quantum affine algebras

We propose factorized difference operators L(u) associated with the twisted quantum affine algebras U_{q}(A^{(2)}_{2n}),U_{q}(A^{(2)}_{2n-1}), U_{q}(D^{(2)}_{n+1}),U_{q}(D^{(3)}_{4}). These operators are shown to be annihilated by a screening operator. Based on a basis of the solutions of the difference equation L(u)w(u)=0, we also construct a Casorati determinant solution to the T-system for U_{q}(A^{(2)}_{2n}),U_{q}(A^{(2)}_{2n-1}).Comment: 15 page

Functional Relations and Analytic Bethe Ansatz for Twisted Quantum Affine Algebras

Functional relations are proposed for transfer matrices of solvable vertex models associated with the twisted quantum affine algebras $U_q(X^{(\kappa)}_n)$ where $X^{(\kappa)}_n = A^{(2)}_n, D^{(2)}_n, E^{(2)}_6$ and $D^{(3)}_4$. Their solutions are obtained for $A^{(2)}_n$ and conjectured for $D^{(3)}_4$ in the dressed vacuum form in the analytic Bethe ansatz.Comment: 14 pages. Plain Te

Solutions of a discretized Toda field equation for DrD_{r} from Analytic Bethe Ansatz

Commuting transfer matrices of $U_{q}(X_{r}^{(1)})$ vertex models obey the functional relations which can be viewed as an $X_{r}$ type Toda field equation on discrete space time. Based on analytic Bethe ansatz we present, for $X_{r}=D_{r}$, a new expression of its solution in terms of determinants and Pfaffians.Comment: Latex, 14 pages, ioplppt.sty and iopl12.sty assume

Quantum Jacobi-Trudi and Giambelli Formulae for Uq(Br(1))U_q(B_r^{(1)}) from Analytic Bethe Ansatz

Analytic Bethe ansatz is executed for a wide class of finite dimensional $U_q(B^{(1)}_r)$ modules. They are labeled by skew-Young diagrams which, in general, contain a fragment corresponding to the spin representation. For the transfer matrix spectra of the relevant vertex models, we establish a number of formulae, which are $U_q(B^{(1)}_r)$ analogues of the classical ones due to Jacobi-Trudi and Giambelli on Schur functions. They yield a full solution to the previously proposed functional relation ($T$-system), which is a Toda equationComment: Plain Tex(macro included), 18 pages. 7 figures are compressed and attache

Creation of ballot sequences in a periodic cellular automaton

Motivated by an attempt to develop a method for solving initial value problems in a class of one dimensional periodic cellular automata (CA) associated with crystal bases and soliton equations, we consider a generalization of a simple proposition in elementary mathematics. The original proposition says that any sequence of letters 1 and 2, having no less 1's than 2's, can be changed into a ballot sequence via cyclic shifts only. We generalize it to treat sequences of cells of common capacity s > 1, each of them containing consecutive 2's (left) and 1's (right), and show that these sequences can be changed into a ballot sequence via two manipulations, cyclic and "quasi-cyclic" shifts. The latter is a new CA rule and we find that various kink-like structures are traveling along the system like particles under the time evolution of this rule.Comment: 31 pages. Section 1 changed and section 5 adde

Analytic Bethe Ansatz for Fundamental Representations of Yangians

We study the analytic Bethe ansatz in solvable vertex models associated with the Yangian $Y(X_r)$ or its quantum affine analogue $U_q(X^{(1)}_r)$ for $X_r = B_r, C_r$ and $D_r$. Eigenvalue formulas are proposed for the transfer matrices related to all the fundamental representations of $Y(X_r)$. Under the Bethe ansatz equation, we explicitly prove that they are pole-free, a crucial property in the ansatz. Conjectures are also given on higher representation cases by applying the $T$-system, the transfer matrix functional relations proposed recently. The eigenvalues are neatly described in terms of Yangian analogues of the semi-standard Young tableaux.Comment: 45 pages, Plain Te

Characters in Conformal Field Theories from Thermodynamic Bethe Ansatz

We propose a new $q$-series formula for a character of parafermion conformal field theories associated to arbitrary non-twisted affine Lie algebra $\widehat{g}$. We show its natural origin from a thermodynamic Bethe ansatz analysis including chemical potentials.Comment: 12 pages, harvmac, 1 postscript figure file, (some confusion on PF Hilbert space was modified) HUTP-92/A06