4 research outputs found
Integrable structure of W_3 Conformal Field Theory, Quantum Boussinesq Theory and Boundary Affine Toda Theory
In this paper we study the Yang-Baxter integrable structure of Conformal
Field Theories with extended conformal symmetry generated by the W_3 algebra.
We explicitly construct various T- and Q-operators which act in the irreducible
highest weight modules of the W_3 algebra. These operators can be viewed as
continuous field theory analogues of the commuting transfer matrices and
Q-matrices of the integrable lattice systems associated with the quantum
algebra U_q(\hat{sl}(3)). We formulate several conjectures detailing certain
analytic characteristics of the Q-operators and propose exact asymptotic
expansions of the T- and Q-operators at large values of the spectral parameter.
We show, in particular, that the asymptotic expansion of the T-operators
generates an infinite set of local integrals of motion of the W_3 CFT which in
the classical limit reproduces an infinite set of conserved Hamiltonians
associated with the classical Boussinesq equation. We further study the vacuum
eigenvalues of the Q-operators (corresponding to the highest weight vector of
the W_3 module) and show that they are simply related to the expectation values
of the boundary exponential fields in the non-equilibrium boundary affine Toda
field theory with zero bulk mass.Comment: LaTeX, 87 pages, 1 figure. Misprints correcte
Universal R-matrix for quantum affine algebras Uq(A2(2)) and Uq(osp(1|2)) with Drinfeld comultiplication
AbstractWe derive an integral formula for the universal R-matrix for the twisted quantum affine algebra Uq(A2(2)) and quantum affine superalgebra Uq(osp(1|2)) with Drinfeld comultiplication
Cherednik algebras and Zhelobenko operators
We study canonical intertwining operators between induced modules of the trigonometric Cherednik algebra. We demonstrate that these operators correspond to the Zhelobenko operators for the affine Lie algebra of type A. To establish the correspondence, we use the functor of Arakawa, Suzuki and Tsuchiya which maps certain modules of the affine Lie algebra to modules of the Cherednik algebra