Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · q-alg/9604012

Bethe Ansatz for Higher Spin XYZ Models --- Low-lying Excitations ---

Takashi Takebe
View original source ↗Read source document ↗Export metadata ↓

Abstract

A higher spin generalization of the XYZ spin chain defined by the fusion procedure is considered. Energy and momentum of the ground state and low-lying excited states of the model are computed by means of an isomorphism between a space of theta functions on which the Sklyanin algebra acts and a space obtained by the fusion procedure.

Explore related subjects

q-algmath.QA

Keep this discovery

BibTeXRIS

Takashi Takebe. 1996-04-19. Bethe Ansatz for Higher Spin XYZ Models --- Low-lying Excitations ---. https://doi.org/10.1088/0305-4470%2F29%2F21%2F026

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2016

Quantization of Lie bialgebras, I

In the paper "On some unsolved problems in quantum group theory", V.Drinfeld formulated the problem of the existence of a universal quantization for Lie bialgebras. When the paper "Tensor structures arising from affine Lie algebras, III", by Kazhdan and Lusztig, appeared, Drinfeld asked whether its methods could be useful for the problem of universal quantization of Lie bialgebras. In this paper we use these methods to construct the universal quantization, which gives a positive answer to Drinfeld's question. We also show the existence of universal quantization of classical r-matrices, unitary r-matrices, and quasitriangular Lie bialgebras, which answers the corresponding questions of Drinfeld.

q-alg↗
arXiv2014

Finite-dimensional Representations of Quantum Affine Algebras

We present a conjecture on the irreducibility of the tensor products of fundamental representations of quantized affine algebras. This conjecture implies in particular that the irreducibility of the tensor products of fundamental representations is completely described by the poles of the R-matrices. The conjecture is proved in certain cases.

q-alg↗
arXiv2005

Zeros and orthogonality of the Askey-Wilson polynomials for q a root of unity

We study some properties of the Askey-Wilson polynomials (AWP) when q is a primitive N-th root of unity. For general four-parameter AWP, zeros of the N-th polynomial and the orthogonality measure are found explicitly. Special subclasses of the AWP, e.g., the continuous q-Jacobi and big q-Jacobi polynomials, are considered in detail. A set of discrete weight functions positive on a real interval is described. Some new trigonometric identities related to the AWP are obtained. Normalization conditions of some polynomials are expressed in terms of the Gauss sums.

q-alg↗