A Monomial Basis for the Virasoro Minimal Series M (p, p′): The Case 1 < p′/p < 2

Quadratic relations are given explicitly in two cases of chiral conformal field theory, and monomial bases of the representation spaces are constructed by using the Fourier components of the intertwiners. The first case is the (2,1) primary fields for the (p, p′)-minimal series M_r,s (1 ≤ r ≤ p - 1, 1 ≤ s ≤ p′ - 1) for the Virasoro algebra where 1 < p′/p < 2. We restrict ourselves to the case p ≥ 3, for which the (2,1) primary field exists. The second case is the intertwiners corresponding to the two-dimensional representation for the level k integrable highest weight modules V(λ) (0 ≤ λ ≤ k) for the affine Lie algebra S-fraktur sign l2.