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On form factors and Macdonald polynomials. (English) Zbl 1342.81187
Summary: We are developing the algebraic construction for form factors of local operators in the sinh-Gordon theory proposed by B. Feigin and the first author [J. Phys. A, Math. Theor. 42, No. 30, Article ID 304014, 32 p. (2009; Zbl 1177.81121)]. We show that the operators corresponding to the null vectors in this construction are given by the degenerate Macdonald polynomials with rectangular partitions and the parameters \(t = -q\) on the unit circle. We obtain an integral representation for the null vectors and discuss its simple applications.

MSC:
81R12 Groups and algebras in quantum theory and relations with integrable systems
05E05 Symmetric functions and generalizations
33D52 Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.)
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