Algebraic Structure of Integrable Field Theories

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1.Algebraic representation of correlation functionsWe obtained an algebraic representation for correlation functions of integrable XXX, XXZ spin chains in which use of multiple integrals is avoided. A similar conjectural formula is also found for the -XYZ chain. The previous formula, obtained through our researches in the last year, is improved to a form applicable to physically important homogeneous chains. For quantum group invariant operators in the XXZ chain only one transcendental function is involved.2.Monomial basis in conformal field theoryWe studied the Virasoro minimal modules M(p, p') with 1 < p'/p < 2.We constructed a monomial basis using the Fourier components of the (2, 1)-primary field, and determined their quadratic relations. We also found conjectural bases in the case p'/p > 2, and for 1 < p'/p <2 using (1, 3)-primary field, and showed that their numbers match the character of the representation space. In the latter case with p'= p + 1 the character is shown to coincide with that of the fusion product of two sl_2-modules.