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 Mosc. Math. J., 2004, Volume 4, Number 4, Pages 787–846 (Mi mmj172)

Counting minimal form factors of the restricted sine-Gordon model

M. Jimboa, T. Miwab, Y. Takeyamac

a University of Tokyo
b Kyoto University
c University of Tsukuba

Abstract: 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 $U_q(\widehat{\mathfrak{sl}}_2)$ 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.

Key words and phrases: Form factor, restricted sine-Gordon model.

DOI: https://doi.org/10.17323/1609-4514-2004-4-4-787-846

Full text: http://www.ams.org/.../abst4-4-2004.html
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Bibliographic databases:

MSC: 81T40, 81R50
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Citation: M. Jimbo, T. Miwa, Y. Takeyama, “Counting minimal form factors of the restricted sine-Gordon model”, Mosc. Math. J., 4:4 (2004), 787–846

Citation in format AMSBIB
\Bibitem{JimMiwTak04} \by M.~Jimbo, T.~Miwa, Y.~Takeyama \paper Counting minimal form factors of the restricted sine-Gordon model \jour Mosc. Math.~J. \yr 2004 \vol 4 \issue 4 \pages 787--846 \mathnet{http://mi.mathnet.ru/mmj172} \crossref{https://doi.org/10.17323/1609-4514-2004-4-4-787-846} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2124168} \zmath{https://zbmath.org/?q=an:1084.81066} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000208595000002} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Feigin B., Feigin E., “Homological realization of restricted Kostka polynomials”, Int. Math. Res. Not., 2005, no. 33, 1997–2029
2. Murakami J., Nagatomo K., “Logarithmic knot invariants arising from restricted quantum groups”, Internat. J. Math., 19:10 (2008), 1203–1213
3. Lashkevich M., Pugai Ya., “Form Factors in Sinh- and sine-Gordon Models, Deformed Virasoro Algebra, Macdonald Polynomials and Resonance Identities”, Nucl. Phys. B, 877:2 (2013), 538–573
4. Lashkevich M., Pugai Ya., “On Form Factors and Macdonald Polynomials”, J. High Energy Phys., 2013, no. 9, 095
5. Murakami J., “Generalized Kashaev Invariants For Knots in Three Manifolds”, Quantum Topol., 8:1 (2017), 35–73