Counting minimal form factors of the restricted sine-Gordon model
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We revisit the issue of counting all local fields of the restricted sine-Gordon model, in the case corresponding to a perturbation of minimal unitary conformal field theory. The problem amounts to the study of a quotient of certain space of polynomials which enter the integral representation for form factors. This space may be viewed as a $q$-analog of the space of conformal coinvariants associated with U_q(sl_{2}^) with q=\sqrt{-1}. We prove that its character is given by the restricted Kostka polynomial multiplied by a simple factor. As a result, we obtain a formula for the truncated character of the total space of local fields in terms of the Virasoro characters.
58 pages, final version, Proposition 2.8 modified
58 pages, final version, Proposition 2.8 modified