The affine infinite-product factorization conjecture for universal K-matrices

Let Υ\Upsilon be the universal K-matrix associated with an affine quantum symmetric pair, and let the quasi-RR-matrix be the corresponding universal quasi-RR-matrix of a quantum affine algebra or Yangian. An infinite-product factorization is a factorization of Υ\Upsilon as an infinite ordered product of factors analogous to the corresponding factorization of the quasi-RR-matrix.

Affine factorization conjecture. In affine type, Υ\Upsilon admits an infinite-product factorization analogous to such a factorization of the quasi-RR-matrix of quantum affine algebras and Yangians.

The conjecture is motivated by the absence of explicit universal K-matrix formulae in the affine case and by the abelian behavior in restricted rank one. The source does not state that this factorization has been proved.

Sources & referencesView supporting material

Primary source

Andrea Appel and Bart Vlaar, “Boundary transfer matrices arising from quantum symmetric pairs”, arXiv:2410.21654 (2025).

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