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A combinatorial interpretation of the scalar products of state vectors of integrable models. (English) Zbl 1307.05222

J. Math. Sci., New York 200, No. 6, 662-670 (2014) and Zap. Nauchn. Semin. POMI 421, 33-46 (2014).
Summary: The representation of Bethe wave functions of certain integrable models via Schur functions allows one to apply the well-developed theory of symmetric functions to the calculation of thermal correlation functions. The algebraic relations arising in the calculation of scalar products and correlation functions are based on the Binet-Cauchy formula for the Schur functions. We provide a combinatorial interpretation of the formula for the scalar products of Bethe state vectors in terms of nests of self-avoiding lattice paths constituting so-called watermelon configurations. The proposed interpretation is, in turn, related to the enumeration of boxed plane partitions.

MSC:

05E05 Symmetric functions and generalizations
81Q40 Bethe-Salpeter and other integral equations arising in quantum theory
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