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arXiv · 2210.17109

Quantum dilogarithm identities arising from the product formula for universal R-matrix of quantum affine algebras

Masaru Sugawara
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Abstract

In arXiv:0912.1346, four quantum dilogarithm identities containing infinitely many factors are proposed as wall-crossing formula for refined BPS invariant. We give algebraic proof of these identities using the formula for universal R-matrix of quantum affine algebra developed by K. Ito, which yields various product presentation of universal R-matrix by choosing various convex orders on affine root system. By the uniqueness of universal R-matrix and appropriate degeneration, we can construct various quantum dilogarithm identities including the ones proposed in arXiv:0912.1346, which turn out to correspond to convex orders of multiple row type.

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BibTeXRIS

Masaru Sugawara. 2022-10-31. Quantum dilogarithm identities arising from the product formula for universal R-matrix of quantum affine algebras. https://doi.org/10.4171/prims%2F59-4-4

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