منابع مشابه
Temperley–Lieb stochastic processes
We discuss one-dimensional stochastic processes defined through the Temperley–Lieb algebra related to the Q = 1 Potts model. For various boundary conditions, we formulate a conjecture relating the probability distribution which describes the stationary state, to the enumeration of a symmetry class of alternating sign matrices, objects that have received much attention in combinatorics. PACS num...
متن کاملTemperley-lieb Immanants
We use the Temperley-Lieb algebra to define a family of totally nonnegative polynomials of the form ∑ σ∈Sn f(σ)x1,σ(1) · · ·xn,σ(n). The cone generated by these polynomials contains all totally nonnegative polynomials of the form ∆J,J′(x)∆L,L′(x)−∆I,I′(x)∆K,K′ (x), where ∆I,I′(x), . . . ,∆K,K′(x) are matrix minors. We also give new conditions on the eight sets I, . . . ,K ′ which characterize d...
متن کاملCyclic representations of the periodic Temperley Lieb algebra, complex Virasoro representations and stochastic processes
An N2 dimensional representation of the periodic Temperley-Lieb algebra TLL(x) is presented. It is also a representation of the cyclic group ZN . We choose x = 1 and define a Hamiltonian as a sum of the generators of the algebra acting in this representation. This Hamiltonian gives the time evolution operator of a stochastic process. In the finite-size scaling limit, the spectrum of the Hamilto...
متن کاملMonomials and Temperley{lieb Algebras
We classify the \fully tight" simply-laced Coxeter groups, that is, the ones whose iji-avoiding Kazhdan{Lusztig basis elements are monomials in the generators B s i. We then investigate the basis of the Temperley{Lieb algebra arising from the Kazhdan{Lusztig basis of the associated Hecke algebra, and prove that the basis coincides with the usual (monomial) basis.
متن کاملTemperley - Lieb Quantum Spin Chains
We solve the spectrum of the closed Temperley-Lieb quantum spin chains using the coordinate Bethe ansatz. These models are invariant under the quantum group U q [sl(2)].
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 2002
ISSN: 0305-4470
DOI: 10.1088/0305-4470/35/45/105