Okounkov's monodromy formula for wall operators

From papers

Let M(z)M(z) be a rational operator defining a quantum difference connection, and let Mon(z)\mathsf{Mon}(z) denote its monodromy. For an integral cocharacter or wall parameter w\mathsf{w}, define

Monw=limq0Mon(a,zqw).\mathsf{Mon}_\mathsf{w}=\lim_{q\to 0}\mathsf{Mon}(a,zq^\mathsf{w}).

Okounkov's wall-operator conjecture. The wall operator is given by

Bw(zshifted)=MonwMonw+ε1.\mathsf{B}_\mathsf{w}(z_\text{shifted})=\mathsf{Mon}_\mathsf{w}\cdot\mathsf{Mon}_{\mathsf{w}+\varepsilon}^{-1}.

This conjecture proposes that individual wall-crossing operators can be reconstructed from asymptotic limits of the monodromy of the quantum difference equation. The source gives no resolution status.

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Sources & referencesView supporting material

Primary source

Iakov Kononov, “Elliptic stable envelopes and 3d mirror symmetry”, arXiv:2106.09888 (2021).

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