منابع مشابه
Quantum Spin Models and Extended Conformal Algebras
First, an algebraic criterion for integrability is discussed {the so-called `superintegrability'{ and some results on the classi cation of superintegrable quantum spin Hamiltonians based on sl(2) are obtained. Next, the massive phases of theZn-chiral Potts quantum spin chain (a model that violates parity) are studied in detail. It is shown that the excitation spectrum of the massive high-temper...
متن کاملSpin Models and Strongly Hyper-Self-Dual Bose-Mesner Algebras
We introduce the notion of hyper-self-duality for Bose-Mesner algebras as a strengthening of formal self-duality. LetM denote a Bose-Mesner algebra on a finite nonempty set X . Fix p ∈ X , and letM∗ and T denote respectively the dual Bose-Mesner algebra and the Terwilliger algebra ofMwith respect to p. By a hyper-duality ofM, we mean an automorphism ψ of T such that ψ(M) =M∗, ψ(M∗) =M; ψ2(A) = ...
متن کاملClifford Algebras and Spin Groups
We’ll now turn from the general theory to examine a specific class class of groups: the orthogonal groups. Recall that O(n,R) is the group of n by n orthogonal matrices (the group preserving the standard inner product on R). This group has two components, with the component of the identity SO(n,R), the orthogonal matrices of determinant 1. We’ll mostly restrict attention to SO(n,R). An importan...
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We show how using Clifford algebras and their representations can greatly simplify the analysis of integrable systems. In particular, we apply this approach to the XX-model with non-diagonal boundaries which is among others related to growing and fluctuating interfaces and stochastic reaction-diffusion systems. Using this approach, we can not only diagonalize the system, but also find new hidde...
متن کاملSpin and Clifford algebras, an introduction
In this short pedagogical presentation, we introduce the spin groups and the spinors from the point of view of group theory. We also present, independently, the construction of the low dimensional Clifford algebras. And we establish the link between the two approaches. Finally, we give some notions of the generalisations to arbitrary spacetimes, by the introduction of the spin and spinor bundles.
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 1999
ISSN: 0195-6698
DOI: 10.1006/eujc.1999.0315