Fe b 20 03 Free field constructions for the elliptic algebra A q , p ( ̂ sl 2 ) and Baxter ’ s eight - vertex model ∗
نویسنده
چکیده
Free field constructions for the elliptic algebra A q,p (sl 2) and Baxter's eight-vertex model Abstract Three examples of free field constructions for the vertex operators of the elliptic quantum group A q,p (sl 2) are obtained. Two of these (for p 1/2 = ±q 3/2 , p 1/2 = −q 2) are based on representation theories of the deformed Virasoro algebra, which correspond to the level 4 and level 2 Z-algebra of Lepowsky and Wilson. The third one (p 1/2 = q 3) is constructed over a tensor product of a bosonic and a fermionic Fock spaces. The algebraic structure at p 1/2 = q 3 , however, is not related to the deformed Virasoro algebra. Using these free field constructions, an integral formula for the correlation functions of Baxter's eight-vertex model is obtained. This formula shows different structure compared with the one obtained by Lashkevich and Pugai.
منابع مشابه
A pr 2 00 3 Free field constructions for the elliptic algebra A q , p ( ̂ sl 2 ) and Baxter ’ s eight - vertex model ∗
Free field constructions for the elliptic algebra A q,p (sl 2) and Baxter's eight-vertex model Abstract Three examples of free field constructions for the vertex operators of the elliptic quantum group A q,p (sl 2) are obtained. Two of these (for p 1/2 = ±q 3/2 , p 1/2 = −q 2) are based on representation theories of the deformed Virasoro algebra, which correspond to the level 4 and level 2 Z-al...
متن کاملNew R - matrices from Representations of Braid - Monoid Algebras based on Superalgebras
In this paper we discuss representations of the Birman-Wenzl-Murakami algebra as well as of its dilute extension containing several free parameters. These representations are based on superalgebras and their baxterizations permit us to derive novel trigonometric solutions of the graded Yang-Baxter equation. In this way we obtain the multiparametric R-matrices associated to the U q [sl(r|2m) (2)...
متن کاملA new Q-matrix in the Eight-Vertex Model
We construct a Q-matrix for the eight-vertex model at roots of unity for crossing parameter η = 2mK/L with odd L, a case for which the existing constructions do not work. The new Q-matrix Q̂ depends on the spectral parameter v and also on a free parameter t. For t = 0 Q̂ has the standard properties. For t 6= 0, however, it does not commute with the operator S and not with itself for different val...
متن کاملar X iv : h ep - t h / 03 09 06 8 v 1 6 S ep 2 00 3 Integrable Lattice Models for Conjugate A ( 1 ) n Roger
A new class of A (1) n integrable lattice models is presented. These are interaction-round-a-face models based on fundamental nimrep graphs associated with the A (1) n conjugate modular invariants, there being a model for each value of the rank and level. The Boltzmann weights are parameterized by elliptic theta functions and satisfy the Yang-Baxter equation for any fixed value of the elliptic ...
متن کاملEMBEDDED ELLIPTIC CURVES AND THE YANG-BAXTER EQUATIONSt
The completely 2, symmetric S-matrix defined by Belavin is shown to satisfy the Yang-Baxter equations. In the projective space of Boltzmann weights, the curves on which there exist commuting transfer matrices are shown to be embedded elliptic curves. Explicit polynomial equations for these curves are given. For n = 2 these results reduce to the results of Baxter for the symmetric eight-vertex m...
متن کامل