Baxter'sQ-operator for theW-algebraW_N

Abstract

The q-oscillator representation for the Borel subalgebra of the affine symmetryBy means of this q-oscillator representation, we give the free field realizations of the Baxter's Q-operator Q j (λ), Q j (λ), (j = 1, 2, · · · , N ) for the W -algebra W N . We give the functional relations of the T -Q operators, including the higher-rank generaliztion of the Baxter's T -Q relation.

Baxter's Q-operators for supersymmetric spin chains

“…In this paper we have developed an algebraic theory of the Q-operators for solvable models associated with the quantized affine algebra U q ( sl(2|1)), extending previously known results for U q ( sl (2)) [4,5] and U q ( sl (3)) [53] (see also [76] and [77] for U q ( sl(n)) case). Our general formalism has been illustrated by two representative cases: the 3-state lattice model and a continuous quantum field theory, associated with the AKNS soliton hierarchy.…”

Bethe ansatz equations for the classical $A^{(1)}_{n}$ affine Toda field theories

“…The functional relation (4.26) is expected to coincide with the dressed vacuum form for one of the transfer matrix eigenvalues of the corresponding massive quantum integrable model. Related functional equations derived for the W N conformal field theory appear in [19].…”

“…This process yields 19) where the operator D n (g) defined in (4.10) is now a function of x. This is precisely the n th -order ODE appearing in the massless SU (n) ODE/IM correspondence [6,7].…”

Classical tau-function for quantum spin chains

“…[45,[52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67]). In this section, we explain how the Baxter Q-operators emerge from the master T -operator using the approach of [12].…”