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Register a new userA $phi_{1,3}$-filtration of the Virasoro minimal series M(p,p) with 1<p/p< 2
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The filtration of the Virasoro minimal series representations M^{(p,p)}_{r,s} induced by the (1,3)-primary field $phi_{1,3}(z)$ is studied. For 1< p/p< 2, a conjectural basis of M^{(p,p)}_{r,s} compatible with the filtration is given by using monomial vectors in terms of the Fourier coefficients of $phi_{1,3}(z)$. In support of this conjecture, we give two results. First, we establish the equality of the character of the conjectural basis vectors with the character of the whole representation space. Second, for the unitary series (p=p+1), we establish for each $m$ the equality between the character of the degree $m$ monomial basis and the character of the degree $m$ component in the associated graded module Gr(M^{(p,p+1)}_{r,s}) with respect to the filtration defined by $phi_{1,3}(z)$.
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We derive the fermionic polynomial generalizations of the characters of the integrable perturbations $phi_{2,1}$ and $phi_{1,5}$ of the general minimal $M(p,p)$ conformal field theory by use of the recently discovered trinomial analogue of Baileys lemma. For $phi_{2,1}$ perturbations results are given for all models with $2p>p$ and for $phi_{1,5}$ perturbations results for all models with ${pover 3}<p< {pover 2}$ are obtained. For the $phi_{2,1}$ perturbation of the unitary case $M(p,p+1)$ we use the incidence matrix obtained from these character polynomials to conjecture a set of TBA equations. We also find that for $phi_{1,5}$ with $2<p/p < 5/2$ and for $phi_{2,1}$ satisfying $3p<2p$ there are usually several different fermionic polynomials which lead to the identical bosonic polynomial. We interpret this to mean that in these cases the specification of the perturbing field is not sufficient to define the theory and that an independent statement of the choice of the proper vacuum must be made.
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